Three Pearls of Number Theory

Three Pearls of Number Theory These 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

  • Title: Three Pearls of Number Theory
  • Author: Aleksandr Yakovlevich Khinchin Aleksandr Yakovlevich Khinchin
  • ISBN: 9780486400266
  • Page: 416
  • Format: Paperback
  • These 3 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.

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    1. According to the opening preface of this book, Khinchin sent these Three Pearls of Number Theory to a former student recuperating during World War II. This is all the backstory that we are given for this. Khinchin claims that any schoolboy should be able to understand this stuff, but does admit that it is quite deep. It’s not that I don’t try to understand, but when I see the long lines of text that are supposed to denote numbers my attention wanders. It is rather shameful for me to say this [...]

    2. Khinchin wrote this book as a letter to a former student of his, wounded during WWII and willing to spend out his recovery with some deep theorems in Arithmetic (Number Theory) whose proofs were “elementary” —not necessarily “simple”.The aforementioned theorems are van der Waerden’s result on arithmetic progressions, the Landau-Schnirelmann hypothesis and Artin and Scherk’s proof of Mann’s theorem concerning densities of sequences of positive integers, and last, but not least, Wa [...]

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