Modular Arithmetic: Calculating with Residue Classes

Abstract

We begin this chapter with a discussion of the principle of division with remainder. In relation to this we shall explain the significance of these remainders, their possible applications, and how one calculates with them. In order for the functions to be introduced later to be understandable, we begin with a bit of algebra.

Every fine story must leave in the mind of the sensitive reader an intangible residuum of pleasure …

—Willa Cather, Not Under Forty, “Miss Jewett”