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2014 Reprint of Original 1952 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. The author, one of the leading Russian mathematicians of the post-war period, attempts to present three important results in number theory in such a way as to promote interest in the subject by showing that elementary number theory is not yet a finished field and that highly interesting new results can still be obtained by ingenious methods. These three puzzles involve the proof of a basic law governing the world of numbers known to be correct in all tested cases - the problem is to prove that the law is always correct. Includes van der Waerden's theorem on arithmetic progressions, the Landau-Schnirelmann hypothesis and Mann's theorem, and a solution to Waring's problem. Proofs and explanations of the answers are provided.

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9781614277477

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