Number Theory

Abstract

This chapter on number theory is truly elementary, although its problems are far from easy. (In fact, here, as elsewhere in the book, we tried to follow Felix Klein’s advice: “Don’t ever be absolutely boring.”) We avoided the intricacies of algebraic number theory, and restricted ourselves to some basic facts about residue classes and divisibility: Fermat’s little theorem and its generalization due to Euler, Wilson’s theorem, the Chinese Remainder Theorem, and Polignac’s formula. Fromall Diophantine equations we discuss linear equations in two variables and two types of quadratic equations: the Pythagorean equation and Pell’s equation.

But first, three sections for which not much background is necessary.