Three Pearls of Number Theory
A. Y. Khinchin
Three diverting 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. The challenges concern 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 included.
