Let $p$ be an odd prime, and for each $x \in \mathbb{Z}$ let $\bar{x}$ denote its residue class in $\mathbb{Z}/p\mathbb{Z}$. Set $G := (\mathbb{Z}/p\mathbb{Z})^\times$, and let $1_G$ denote the identity element of $G$. Let $g,a,k \in \mathbb{Z}$. Suppose that $\bar{g}$ generates the multiplicative group $G$. If $p \nmid a$ and