Solvability of a system of polynomial equations modulo primes

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY（2022）

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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 is an element of Z[x] such that F is solvable modulo p if and only if the equation D(x) 0 (mod p) has a solution.

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Key words

prime numbers, polynomial congruences, prime divisors of polynomials, algebraic numbers

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