Synopses & Reviews
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 included.
Faced with the unrelieved tedium of a hospital stay, a Russian soldier recuperating from his World War II injuries begged one of his former instructors for something to occupy his mind. The professor replied with "Three Pearls of Number Theory", a trio of mathematical problems as absorbing today as they were more than 50 years ago.
Table of Contents
A LETTER TO THE FRONT (IN LIEU OF A PREFACE)
VAN DER WAERDEN'S THEOREM ON ARITHMETIC PROGRESSIONS
THE LANDAU-SCHNIRELMANN HYPOTHESIS AND MANN'S THEOREM
AN ELEMENTARY SOLUTION OF WARING'S PROBLEM