Unsolved problems in number theory在数论中未解决的问题
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作者： Richard K. Guy著
出 版 社：
出版时间： 2004-6-1字数：版次： 1页数： 437印刷时间： 2004/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387208602包装： 精装内容简介
Mathematics is kept alive by the appearance of new unsolved problems, problems posed from within mathematics itself, and also from the increasing number of disciplines where mathematics is applied. This book provides a steady supply of easily understood, if not easily solved, problems which can be considered in varying depths by mathematicians at all levels of mathematical maturity.
For this new edition, the author has included new problems on symmetric and asymmetric primes, sums of higher powers, Diophantine m-tuples, and Conway's RATS and palindromes. The author has also included a useful new feature at the end of several of the sections: lists of references to OEIS, Neil Sloane's Online Encyclopedia of Integer Sequences.
目录
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Glossary of Symbols
Introduction
A.Prime Numbers
A1.Prime values of quadratic functions
A2. Primes connected with factorials
A3. Mersenne primes. Repunits. Fermat numbers. Primes of shape k 2n + 1
A4. The prime number race
A5. Arithmetic progressions of primes
A6. Consecutive primes in A.P.
A7. Cunningham chains
A8. Gaps between primes. Twin primes
A9. Patterns of primes
A10. Gilbreath's conjecture
A11. Increasing and decreasing gaps
A12.Pseudoprimes. Euler pseudoprimes. Strong pseudoprimes
A13. Carmichael numbers
A14. "Good'' primes and the prime number graph
A15. Congruent products of consecutive numbers
A16. Gaussian and Eisenstein-Jacobi primes
A17. Formulas for primes
A18.The Erdos-Selfridge classification of primes
A19.Values of n making n -- 2k prime. Odd numbers not of the form ±pa ±2b
A20.Symmetric and asymmetric primes
……
B Divisibility 71
C Additive number theory
D Diophantine equations
E Sequences of integers
F None of the above
