The distribution of powers of primes related to the Frobenius problem

Enxun Huang, Tengyou Zhu

Let $1<c<d$ be two relatively prime integers, $g_{c,d}=cd-c-d$ and $\mathbb{P}$ is the set of primes. For any given integer $k\ge 1$, we prove that $$\#\left\{p^k\le g_{c,d}:p\in…