On some congruence with application to exponential sums

Abstract

We will study the solution of a congruence, $x\equiv g^{(1/2){\omega }_g(2^n)}\mathrm{mod}{2}^n$, 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.

6 pages, no figures, no tables