Monomial congruences

Abstract

Letn ₁,n ₂,...,n _t integers. It is proved that the monomial congruence$x_1^{n_1 } x_2^{n_2 } \ldots x_t^{n_t } \equiv a (\bmod m)$ is solvable for allm≥2 and (a, m)=1 if and only if (n ₁ ,n ₂ ..., n _t )=1.