On the Non-negative Integer Solutions to Diophantine Equations $F_n-F_m=7^a$ and $F_n-F_m=13^a$

Gaha Anouar, Mezroui Soufiane

In this paper, we study the solutions of the equation $F_n-F_m=p^a$ where $p$ is either $7$ or $13$ and $n>m⩾0$, $a⩾2$. We confirm the conjecture of Erduvan and K…