ABSTRACT
As far as divisibility is concerned, there are three kinds of integers: zero, units, and primes. This chapter examines the units in the various commutative and polynomial rings. It discusses the Bézout’s equation for relatively prime integers. The chapter explains the properties of congruence to understand an old trick about division by 9 and division by 11. It describes the Wilson's theorem proving that if p is a prime integer, then each nonzero element of a polynomial ring has an inverse. The chapter discusses the application of the Dirichlet pigeonhole principle and also proves a theorem related to quadratic residues.
