104 Number Theory Problems: From the Training of the USA IMO TeamSpringer Science & Business Media, 5 d’abr. 2007 - 204 pàgines This book contains 104 of the best problems used in the training and testing of the U. S. International Mathematical Olympiad (IMO) team. It is not a collection of very dif?cult, and impenetrable questions. Rather, the book gradually builds students’ number-theoretic skills and techniques. The ?rst chapter provides a comprehensive introduction to number theory and its mathematical structures. This chapter can serve as a textbook for a short course in number theory. This work aims to broaden students’ view of mathematics and better prepare them for possible participation in various mathematical competitions. It provides in-depth enrichment in important areas of number theory by reorganizing and enhancing students’ problem-solving tactics and strategies. The book further stimulates s- dents’ interest for the future study of mathematics. In the United States of America, the selection process leading to participation in the International Mathematical Olympiad (IMO) consists of a series of national contests called the American Mathematics Contest 10 (AMC 10), the American Mathematics Contest 12 (AMC 12), the American Invitational Mathematics - amination (AIME), and the United States of America Mathematical Olympiad (USAMO). Participation in the AIME and the USAMO is by invitation only, based on performance in the preceding exams of the sequence. The Mathematical Olympiad Summer Program (MOSP) is a four-week intensive training program for approximately ?fty very promising students who have risen to the top in the American Mathematics Competitions. |
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104 Number Theory Problems: From the Training of the USA IMO Team Titu Andreescu,Dorin Andrica,Zuming Feng Previsualització no disponible - 2006 |
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answer appears apply arithmetic progression assume assumption balls base called claim clear Clearly common complete set composite compute conclude congruent consecutive consider consists contains contradiction Corollary cube defined denote desired Determine difficult digits divides divisible divisors elements ends equal equation establish exactly Example exists expressed fact Find follows fractions function gcd(a gcd(m gcd(n given gives greater greatest Hence implying increasing induction inequality infinitely integer n interesting largest leading least Mathematical Olympiad modulo multiple nonnegative integers nonzero Note obtain odd integer pair perfect square points positive integer possible prime divisor prime factors problem Proof Proposition Prove relation relatively prime remainder representation residue classes modulo result sequence set of residue side smallest Solution subset Suppose true unique weights write written