SOLVABILITY OF A SYSTEM OF POLYNOMIAL EQUATIONS MODULO PRIMES
Olli Järviniemi · Bulletin of the Australian Mathematical Society · 2022
Abstract Let F be a system of polynomial equations in one or more variables with integer coefficients. We show that there exists a univariate polynomial $D \in \mathbb {Z}[x]$ such that F is solvable modulo p if and only if the equation $D(x) \equiv 0 \pmod {p}$ has a solution.