Definition:Polynomial Congruence/Number of Solutions

Definition

Let:

$\map P x \equiv 0 \pmod n$

be a polynomial congruence.

Let $S = \set {b_1, b_2, \ldots, b_n}$ be a complete set of residues modulo $n$.

The number of solutions of $\map P x \equiv 0 \pmod n$ is the number of integers $b \in S$ for which $\map P b \equiv 0 \pmod n$.