Counting Solutions of Congruences

Abstract

In this chapter we shall use the results obtained in the preceding chapter to count solutions of certain linear and other congruences in s unknowns. By a solution of a congruence, with modulus r, we mean a solution (mod r), i.e., an ordered s-tuple of integers (x₁,…, x_s) that satisfies the congruence, with two s-tuples (x₁,…, x_s) and $\langle x_1^{'},...,x_s^{'}\rangle$ that satisfy the congruence counted as the same solution if and only if x_i ≡ x₁′. (mod r) for i = 1,…, s.