2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70369We will study the solution of a congruence, $x \equiv g^{(1/2)ω_g(2^n)} \bmod 2^n$, depending on the integers $g$ and $n$, where $ω_g(2^n)$ 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 tablesNumber Theorytext