Definition:Polynomial Congruence/Number of Solutions
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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 $\map P b \equiv 0 \pmod n$.