Lagrange theorem for polynomial congruences
= Lagrange theorem for polynomial congruences
{c}
A nonzero polynomial of degree $d$ over a field has at most $d$ roots. In particular, if a polynomial congruence $f(x)\equiv0\pmod p$ has degree $d$ and not all coefficients are divisible by the prime $p$, it has at most $d$ incongruent solutions modulo $p$.