Sep 1, 2011
Maths at sistemasnumericos2011.files.wordpress.com
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Bloch E.D. Proofs and Fundamentals.. A First Course in Abstract ...
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J. I t. Fir. 338 8. Number Systems. 8.3.5. [Used in Section 6.1.] Letn E N and let f: [[1,n]] —-> N be a map. Show that there is some k e {[1, 11]} such that f(k) 3 f (1') ...
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Stewart I. Galois Theory (3ed., CRC, 2004)(T)(323s)(ISBN ...
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Chapter 3. Factorization of Polynomials. Not only is there an algebra of polynomials, there is an arithmetic. That is, there ...
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Complex Numbers and the Complex Plane
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Complex Numbers and the. Complex Plane. 1. Riemann surface for arg(z). See page 97. 3π. 2π. –2π. –3π π. –π. –1. –1. 1. 1. 0. 0. 0. 1.1. Complex Numbers and ...
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Universidad Nacional de Colombia Sistemas numéricos Programa I ...
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Universidad Nacional de Colombia. Sistemas numéricos. Programa. I - 2011. John Jaime Rodríguez jjrodriguezv@unal.edu.co oficina 315 edificio 404 ...
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Universidad Nacional de Colombia Sistemas numéricos Programa II ...
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Universidad Nacional de Colombia. Sistemas numéricos. Programa. II - 2011. John Jaime Rodríguez jjrodriguezv@unal.edu.co oficina 315 edificio 404 ...
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Schaum's Outline of Combinatorics.djvu
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Chapter 1. Basic Tools. 1.1 THE SUM RULE AND TI-IE PRODUCT RULE. How many arrangements of a specified kind can be undergone by a given set of ...
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CONSTRUCTION OF R
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CONSTRUCTION OF R. 1. MOTIVATION. We are used to thinking of real numbers as successive approximations. For example, we write π = 3.14159 . ...
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Bloch E.D. Proofs and Fundamentals.. A First Course in Abstract ...
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256 7. Selected Topics integer. Every element of Q — {0} has an inverse with respect to multipli- cation, nameiy its reciprocal. ...
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LISTAS numerico 2011.xlsx
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codigo documento. Taller 1. Taller 2. 1133359 1030550012. 4,1. 3,5. 1133466 1014223009. 4,1. 3,5. 1153448 79837810. 0,0. 0,0. 1153482 1022943157. 4,3 ...
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Bloch E.D. Proofs and Fundamentals.. A First Course in Abstract ...
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2 Jul 2011 – as. 256 7. Selected Topics integer. Every element of Q —- {0} has an inverse with respect to multipli- cation, nameiy its reciprocal. (2) Let GL2 ...
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264 7. Selected Topics
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i i. 264 7. Selected Topics without changing its appearance. Denote the reflections through these lines by M1, M; and M3. For exampie, if we apply M2 to the ...
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Theorem 4.8 Chinese Remainder Theorem. Let n1 , n2, . . . , n, be ...
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Theorem 4.8 Chinese Remainder Theorem. Let n1 , n2, . . . , n, be positive integers such that gcd(n,- , nj) : 1 fori gé j. Then the system of linear congruences ...
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Lista sistemas numéricos.xlsx
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codigo. P1. P2. P3. T1. T2. Q1. T3. T4. T5. DefT. DEF. 1133359. 2,5. 2,3. 2,3. 4,1. 3,5. 5,0. 5,0. 5,0. 5,0. 4,6. 2,9. 1133466. 3,5. 1,9. 2,9. 4,1. 3,5. 4,5. 5,0. 5,0. 5,0 ...
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Rudin W. Principles of Mathematical Analysis.djvu
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1. THE REAL AND COMPLEX NUMBER SYSTEMS. INTRODUCTION. A satisfactory discussion of the main concepts of analysis (such as convergence, ...
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Schaum's Outline of Combinatorics.djvu
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Chapter 1. Basic Tools. 1.1 THE SUM RULE AND TI-IE PRODUCT RULE. How many arrangements of a specified kind can be undergone by a given set of objects? ...
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Bloch E.D. Proofs and Fundamentals.. A First Course in Abstract ...
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8. Number Systems. The integers have been made by God. All else is the work of l man. Leopold Kronecker (1823-1891). 8.1 Back to the Beginning. We end our ...
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Burton D. Elementary Number Theory, 6th Edition.djvu
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DIVISIBILITY THEORY IN THE INTEGERS. 2.2 THE DIVISION ALGORITHM. We have been exposed to relationships between integers for several pages and, as ...
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Bloch E.D. Proofs and Fundamentals.. A First Course in Abstract ...
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.1. 1 r. F: 338 8. Number Systems. 8.3.5. [Used in Section 6.1.] Let rt G N and iet f: [[1,n]] —~> N be a map. Show that there is some k <5 [[1, 11]] such that f(k) 2 ...
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Untitled - Wordpress Wordpress
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Page 1. Page 2.
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Quiz 3.xlsx
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codigo. Taller 1. Taller 2. Quiz 1. 1133359. 4,1. 3,5. 4,0. 1133466. 4,1. 3,5. 3,5. 1153448. 0,0. 0,0. 0,0. 1153482. 4,3. 0,0. 4,0. 1153515. 4,6. 4,0. 3,5. 1153553 ...
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Tignol J-P. Galois Theory of Algebraic Equations.djvu
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Chapter 7. Roots of Unity. 7.1 Introduction. New branches of mathematics, such as analytic geometry and differential calculus, came into being during the ...
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Taller para el jueves 31 de marzo 1. 2. 3.
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Page 1. Taller para el jueves 31 de marzo. 1. 2. 3.
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Untitled - Wordpress Wordpress
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Page 1. Page 2. Page 3.
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Untitled - Wordpress Wordpress
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Page 1. Page 2.
BMO Questions
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[PDF]Areal Co-ordinate Methods in Euclidean Geometry
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Areal Co-ordinate Methods in Euclidean Geometry. Tom Lovering. April 11, 2008. Introduction. In this article I aim to briefly develop the theory of areal (or ...
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BMO problems from the past (1993 ... - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are ...
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BRITISH MATHEMATICAL OLYMPIAD 1974
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BRITISH MATHEMATICAL OLYMPIAD 1974. Time allowed: 3 hours. Each question should be answered on a fresh sheet of paper. Use one side of the paper ...
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BRITISH MATHEMATICAL OLYMPIAD, 1975 24th March, 1975 Time ...
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BRITISH MATHEMATICAL OLYMPIAD, 1975. 24th March, 1975. Time allowed — 3 hours. Write on one side of the paper only. Start each question on a fresh ...
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. BRITISH MATHEMATICAL OLYMPIAD. Wednesday 17th January 1990. Time allowed - Three and a halt hours ...
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Friday, 30 November 2007 - British Mathematical Olympiad
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30 Nov 2007 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Friday, 30 November 2007. Time allowed 31. 2 hours. ...
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British Mathematical Olympiad 2010/11 British Mathematical ...
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2 Dec 2010 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 2 December 2010. Time allowed 31. 2 hours. ...
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25 February 2003 - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 25 February 2003. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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13 January 1999 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 13 January 1999. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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British Mathematical Olympiad Round 1 Friday 1 December 2006 ...
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UKMT Maths Challenges Office, School of Mathematics, University of Leeds, Leeds LS2 9JT. Tel: 0113 343 2339 Fax: 0113 343 5500 Email: ...
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British Mathematical Olympiad 2005/6 British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 30 November 2005. Time allowed 31. 2 hours. Instructions • Full written solutions - not just ...
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British Mathematical Olympiad 2004/5 British Mathematical Olympiad ...
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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 1 December 2004. Time allowed Three and a half hours. ...
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BRITISH MATHEMATICAL OLYMPIAD
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 15th January 1992. Time allowed. Instructions 0. Three and a half hours. ...
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Thursday, 4 December 2008 - British Mathematical Olympiad
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4 Dec 2008 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 4 December 2008. Time allowed 31. 2 hours. ...
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9th Chinese Girls' Mathematics Olympiad Shijiazhuang, China Day I ...
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10 Aug 2010 – 9th Chinese Girls' Mathematics Olympiad. Shijiazhuang, China. Day I. 8:00 AM - 12:00 PM. August 10, 2010. 1. Let n be an integer greater than ...
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EGMO | 2012
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European Girls' Mathematical Olympiad. EGMO | 2012. UK Mathematical Olympiad for Girls. 23 June 2011. Instructions. Supported by. • Time allowed: 3 hours. ...
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BRITISH MATHEMATICAL ... - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17 January 2001. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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15 February 1996 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 15 February 1996. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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1 February 2005 - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 1 February 2005. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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British Mathematical Olympiad 2009/10 British Mathematical ...
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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 28 January 2010. Time allowed Three and a half hours. Each question ...
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British Mathematical Olympiad 2008/9 British Mathematical Olympiad
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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 29 January 2009. Time allowed Three and a half hours. Each question ...
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BMO Round 2 paper - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 30 January 2007. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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Wednesday 16th January 1991
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2. BRITISH MATHEMATICAL OLYMPIAD. Wednesday 16th January 1991. Time allowed - Three and a half hours. Instructions: ' ...
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¢¡¤£¦¥¨§ © § ¡ !£ ©" # $%£& ©"$'¥ ( )0)1 ¥¨2 34¡¤§ 576869) 6A@ABC ...
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)0)1 ¥¨2 34¡¤§. 576869). 6A@ABC)EDGFH)E5IBQP"D. RTS. UWVEX`Y% aQb' YcVedf bhgiXqprpQdsbtY4 uwvEg x8d¤y €ƒ‚ bh„GvEXTyhdHb a…Ÿ arb' †8€‡bcbhaQxEpQd1 Yh€ˆ ...
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NATIONAL OQ'1MI'I'I'EE FOR MATHEMATICAL CONTESTS
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NATIONAL OQ'1MI'I'I'EE FOR MATHEMATICAL CONTESTS. Further International Selection Test. Friday 5th February 1988. Time allowed - 355 hours. PLEASE ...
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BMO Round 2 paper - British Mathematical Olympiad
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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 31 January 2008. Time allowed Three and a half hours. Each question ...
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International Mathematical Olympiad
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Language: English. Day: 1. Monday, July 18, 2011. Problem 1. Given any set A = {a1,a2,a3,a4} of four distinct positive integers, we denote the sum a1 +a2 +a3 ...
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23 February 2000 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Wednesday, 23 February 2000. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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27 February 1997 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 27 February 1997. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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13 January 1993 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 13th January 1993. Time allowed Three and a half hours. Instructions • Full written solutions are ...
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British Mathematical Olympiad 2009/10 British Mathematical ...
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3 Dec 2009 – United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 1 : Thursday, 3 December 2009. Time allowed 31. 2 hours. ...
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17 January 1996 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 17th January 1996. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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5 December 2001 - British Mathematical Olympiad
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British Mathematical Olympiad. Round 1 : Wednesday, 5 December 2001. Time allowed Three and a half hours. Instructions • Full written solutions - not just ...
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25 February 1999 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 25 February 1999. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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26 February 2002 - British Mathematical Olympiad
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British Mathematical Olympiad. Round 2 : Tuesday, 26 February 2002. Time allowed Three and a half hours. Each question is worth 10 marks. Instructions • Full ...
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British Matheruatical Olympiad 14th March, 1979 Time 8.110§:?£d ...
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NATIONAL CQN1-iI'I"i'EE FUR l'§¢5rTl'lEF.'ATICAI. COFYTESTS. British Matheruatical Olympiad. 14th March, 1979. Time 8.110§:?£d - 3% hours. Write an one ...
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27 February 2001 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Tuesday, 27 February 2001. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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British Mathematical Olympiad 2010/11 British Mathematical ...
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United Kingdom Mathematics Trust. British Mathematical Olympiad. Round 2 : Thursday, 27 January 2011. Time allowed Three and a half hours. Each question ...
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PLEASE READ THESE INSTRUCTIONS CAREFULLY 2
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTES'I'S. British Mathematical Olympiad. Friday 20th November 1987. Time allowed - 3% hours ...
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BMO Round 1 paper - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 1 : Friday, 1 December 2006. Time allowed 31. 2 hours. Instructions • Full written solutions - not just ...
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FURTHER INTERNATIONAL SELECTION TEST
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FURTHER INTERNATIONAL SELECTION TEST. May 5th, 1975 3% hours. 1. In this question a "real function" means a function f such that f(x) exists and is real ...
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15 January 1997 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 15 January 1997. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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14 January 1998 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 14 January 1998. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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International Mathematical Olympiad
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16 Jul 2009 – Wednesday, July 15, 2009. Problem 1. Let n be a positive integer and let a1,...,ak (k ≥ 2) be distinct integers in the set. {1,...,n} such that n ...
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BRITISH MATHEMATICAL OLYMPIAD BRITISH MATHEMATICAL ...
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday 18th January 1995. Time allowed Three and a half hours. Instructions • Full written solutions are ...
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12 January 2000 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 1 : Wednesday, 12 January 2000. Time allowed Three and a half hours. Instructions • Full written solutions - not ...
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Friday, 23rd March 1984
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Further International Selection Test. Friday, 23rd March 1984. Time allowed - 3} hours. Write on ...
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24 February 2004 - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 24 February 2004. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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British Mathematical Olympiad 2002/3 British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 1 : Wednesday, 11 December 2002. Time allowed Three and a half hours. Instructions • Full written ...
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British Mathematical Olympiad
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NATIONAL CUMMITTEE FOR MATHEMATICAL CUNTESTS. British Mathematical Olympiad. Tuesday 4th March 1986. Time allowed ~ 3ž hours . Write on one ...
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National Committee for Mathematical Contests Second International ...
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National Committee for Mathematical Contests. Second International Selection Test. Reading, 23rd April 1988. Time allowed : 355 hours ...
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BMO2 2006 - British Mathematical Olympiad
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Supported by. British Mathematical Olympiad. Round 2 : Tuesday, 31 January 2006. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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13:11 March, 1980
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. 13:11 March, 1980. Time allowed - 3% hours. Write on one side of the paper only ...
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. BRITISH MATHEMATICAL OLYMPIAD. Tuesday 13th December 1988. Time allowed - 3% hours ...
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British Mathematical Olympiad Tuesday 5 March, 1985
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Tuesday 5 March, 1985. Time allowed - 3% hours. Write on one ...
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Q1 Let x1,x2,. . .xn be real numbers such that 0' xig 2 £01
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FIST 2, Bristol , May, 1985. Q1 Let x1,x2,. . .xn be real numbers such that 0' xig 2 £01- each 1. . Prove that. n n. E 3% [xi-xii Q n? ...
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24 February 1994 - British Mathematical Olympiad
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 24 February 1994. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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Write on one side of the paper onZy. Start each question on a
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Tuesday, 13th March l984. Time allowed ~ 3% hours. Write on one ...
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THE MATHEMATICAL ASSOCIATION National Committee for ...
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THE MATHEMATICAL ASSOCIATION. National Committee for Mathematical Contests. British Mathematical Olympiad. 10th March 1983. Time allowed — 3% ...
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BRITISH MATHEMATICAL OLYMPIAD BRITISH MATHEMATICAL ...
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BRITISH MATHEMATICAL OLYMPIAD. Round 2 : Thursday, 16 February 1995. Time allowed Three and a half hours. Each question is worth 10 marks. ...
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. Second International Selection Test. Reading, Saturday 10th May 1.986. 3% hours ...
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS
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NATIONAL COMMITTEE FOR MATHEMATICAL CONTESTS. British Mathematical Olympiad. Friday 20th March 1987. Time allowed — 3'/2 hours. PLEASE ...
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2 June 2010
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2 Jun 2010 – NST 4. 2 June 2010. 1. Consider the sequence (ai) such that a0 = 4, a1 = 22 and an − 6an−1 + an−2 = 0 for n ≥ 2. Prove that there are integral ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2011 IMO ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2011 IMO Team Training. Exam T14. • Each question is worth 7 points. • Time allowed is 41. 2 hours. ...
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'h'in.ity College, Cambridge, 14th April 1991
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SECOND INTERNATIONAL SELECTION TEST. 'h'in.ity College, Cambridge, 14th April 1991. Time allowed: Three-and-a-half hours. ...
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GEIMETRY TEST
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NATIONAL (XX“MI'I'I'EE KR MATHE4ATICAL CDNTESTS. Training Weekend 1989. GEIMETRY TEST. Tine allowed = IX hours. A, B are two points on a sphere whose centre ...
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First Selection Test
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First Selection Test. April 2003. 1. Consider triangle ABC. Let U,V,W be points such that U is on the line through B and C, V is on the line through C and A ...
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r1.-iy 12th 1918 — 3% hours
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r1.-iy 12th 1918 — 3% hours. A plane convex pentagon ABCDE is said to have the "unit triangle preperty" if the area of each of the triangles ABC , BCD, CUE, ...
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First Selection Test: Paper 1
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First Selection Test: Paper 1. Trinity College, Cambridge. 16th April 2011. 1. Let ABC be an acute triangle with D, E, F the feet of the altitudes lying on BC, CA, AB ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2008 IMO ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2008 IMO Team Training. Exam T15. • Each question is worth 7 points. • Time allowed is 41. 2 hours. ...
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2009 United Kingdom & Australia Pre-IMO Camp Trinity College ...
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2009 United Kingdom & Australia Pre-IMO Camp. Trinity College, Cambridge. 2nd Test. Thursday 9 July. The Ashes. • Each question is worth 7 points. ...
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1. 2 3. FINAL SELECTION TEST SUNDAY 31 MARCH 1996
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1. 2. 3. FINAL SELECTION TEST. SUNDAY 31 MARCH 1996. Time Allowed: 451- hours. Two circles F1 and I'; intersect at D and E. ...
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Oundle Selection Test 1
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1. 2. 3. Oundle Selection Test 1. 4 hours 30 minutes. Find all nondecreasing functions f : R —> R such that. (1%) f(0) =0, f(1) = 1; ...
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Next Selection Test: Paper 3
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Next Selection Test: Paper 3. Oundle School. 31st May 2011. 1. If X is a set of integers, define D(X) to be the set of differences between elements of X: D(X) = {n ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE 2010 IMO ...
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AUSTRALIAN MATHEMATICAL OLYMPIAD COMMITTEE. 2010 IMO Team Training. Exam T16. • Each question is worth 7 points. • Time allowed is 41. 2 hours. ...
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1 2 5 4.
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1. 2. 5. 4. Further International Selection Test. May l'7, 1972. Time 5 Fours. Only your best 5 answers will score,. Show ho-sf to assign to the vertices of a regular ...
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Next Selection Test: Exam 1
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Next Selection Test: Exam 1. IMO camp, Oundle School. 25-v-2008. Problem 1 Let M and N be vertices of a cube. Assign the number 1 to ...
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Cambridge, 16th April 1989
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NATIGJAL (X1'MI'I'l'E'.E FCR MATHE'!ATICAL (XNTBSTS. Second International Selection Test. Cambridge, 16th April 1989. Tine allowed = 3% hours ...
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FINAL SELECTION TEST SUNDAY 5 APRIL 1998
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1. 2. 3. FINAL SELECTION TEST. SUNDAY 5 APRIL 1998. Time allowed: 4% hours. Let P(:c) be a polynomial with real coefficients such that ...
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NST 2, Eton and Oundle, 2009
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1. 2. 3. NST 2, Eton and Oundle, 2009. There are 2008 red cards and 2008 white cards. They are shuffled and dealt to 2008 people seated facing inwards in a ...
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Next Selection Test: Paper 2
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Next Selection Test: Paper 2. Oundle School. 30th May 2011. 1. Find all functions f : Z → Z such that: (a) f(x + f(x + 2y)) = f(2x) + f(2y) for all integers x, y;. (b) f(0) ...
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Oundle Test 3
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1. 2. 3. Oundle Test 3. 29 May 2007. Let ABC be a triangle with LB 7-4 LC. The incircle I of ABC touches the sides BC, CA AB at the points D, E, F , respectively. ...
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TEAM SELECTION TEST 2 TUESDAY 29 MAY 2001 08.30-13.00 1 ...
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TEAM SELECTION TEST 2. TUESDAY 29 MAY 2001. 08.30-13.00. 1. Let a, b, c, x, y, z be positive reals, with a ≥ b ≥ c and x ≥ y ≥ z. Prove that a2x2 ...
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Next Selection Test: Paper 4
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Next Selection Test: Paper 4. Oundle School. 1st June 2011. 1. Let A be the set of all integers of the form a2 + 13b2, where a and b are integers and b is nonzero ...
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Romanian Master in Mathematics
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Romanian Master in Mathematics. Unofficial Edition, 2008, Bucharest. Problem 1. Let ABC be an equilateral triangle. P is a variable point internal to the triangle ...
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Next Selection Test: Paper 1
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Next Selection Test: Paper 1. Oundle School. 29th May 2011. 1. Circles Γ1 and Γ2 meet at M and N. Let A be on Γ1 and D on Γ2. The lines AM and AN meet Γ2 ...
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UK IMO Next Selection Test 1
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UK IMO Next Selection Test 1. Oundle 2006. 1. Does there exist a bounded function f : R → R with f(1) > 0 satisfying f(x + y)2 ≥ f(x)2 + f(2xy) + f(y)2 ...
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NST3 2009
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1. 2. 3. NST3 2009. Eton May 21, Oundle May 26. Let ABC be an acute-angled triangle, and M be a point in its plane distinct from the vertices. Show that the ...
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First Selection Test: Exam 2
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First Selection Test: Exam 2. IMO camp, Trinity College Cambridge. 2-iv-2007. Problem 1 Let <1, b be positive integers such that for every positive integer ...
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Oundle Test 4
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1. 2. 3. Oundle Test 4. 30 May 2007. Consider triangle ABC'. B1 is on the line AC and the line BB1 passes through the incentre I. The point C1 is similarly defined ...
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FINAL SELECTION TEST SUNDAY )) APRIL )999 08. )5-)2 .4 5 1. A ...
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FINAL SELECTION. TEST. SUNDAY. )) APRIL )999. 08. )5-)2 .4 5. 1. A sequence of positive integers ai, a2, . . . is defined as follows: ai = 1 and, for n > 1, ...
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FST1 2006
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1. 2. 3. FST1 2006. Trinity College Cambridge. Let E be the intersection of the diagonals of the cyclic quadrilateral ...
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Next Selection Test: 4 hours 30 minutes
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Next Selection Test: 4 hours 30 minutes. Oundle, May 27, 2003. Let p1,p2, . . . , pn be distinct prime numbers greater than 3. Show that ...
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First Selection Test: Paper 2
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First Selection Test: Paper 2. Trinity College, Cambridge. 18th April 2011. 1. For any positive integer n, let an be the exponent of the largest power of 2 which ...
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FST2 2009
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FST2 2009. OCR. TCC April 6. 1. Triangle ABC has a right-angle at C, and the point M' on AB is strictly between A and B. Let S, S1 and S2 denote the ...
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British Mathematical Olympiad Round 1 Thursday 2nd December ...
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UKMT, School of Mathematics Satellite, University of Leeds, Leeds LS2 9JT. Tel: 0113 343 2339 Fax: 0113 343 5500 Email: enquiry@ukmt.org.uk Web: ...
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UK IMO FST1
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UK IMO FST1. Trinity College, Cambridge. 9 April 2005. 1. An infinite sequence a0,a1,a2,... of real numbers satisfies the condition ...
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FST 1 2010
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FST 1 2010. Trinity College, Cambridge. 10th April 2010. 1. Find all polynomials P(x) with real coefficients which have the property that if a is a real number and ...
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FST 2 2010
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FST 2 2010. Trinity College, Cambridge. 12th April 2010. 4. Find all solutions to p(p + 1) + q(q + 1) = n(n + 1) where p and q are prime numbers and n is a ...
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