Transcription of 250 PROBLEMS IN ELEMENTARY NUMBER THEORY
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250 PROBLEMS IN ELEMENTARY NUMBER THEORY
250 PROBLEMS IN ELEMENTARY NUMBER THEORY WACLAW SIERPINSKI ISBN ().444.()()()71 2 250 PROBLEMS , in ELEMENTARY NUMBER THEORY .-WACLAW SIERPINSKI "250 PROBLEMS in ELEMENTARY NUMBER THEORY " presents PROBLEMS and their solutions in five specific areas of this branch of mathe-matics: divisibility of numbers, relatively prime numbers, arithmetic progressions, prime and composite numbers, and Diophantic equations. There is, in addition, a section of miscellaneous PROBLEMS . Included are PROBLEMS on several levels of difficulty-some are relatively easy, others rather complex, and a NUMBER so abstruse that they originally were the subject of scientific research and their solutions are of comparatively recent date. All of the solutions are given thoroughly and in detail; they contain information on possible generaliza-tions of the given problem and further indicate unsolved PROBLEMS associated with the given problem and solution.
PROBLEMS I. DIVISIBILITY OF NUMBERS 1. Find all positive integers n such that n2+ 1 is divisible by n+ 1. 2. Find all integers x #= 3 such that x-3Ix3-3. 3. Prove that there exists infinitely many positive integers n such that 4n2+ 1 is divisible both by 5 and 13. 4.
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