On some congruence with application to exponential sums

Abstract

We will study the solution of a congruence, x equivalent to g((1/2)omegag(2n)) mod 2(n), depending on the integers g and n, where omega(g)(2(n)) denotes the order of g modulo 2(n). Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.