On some congruence with application to exponential sums

Soon-Mo Jung

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 $2^n$. M…