BALKAN-SL 2015 N3

Let $a$ be a positive integer. For all positive integer n, we define $a_n=1+a+a^2+\ldots+a^{n-1}.$ Let $s,t$ be two different positive integers with the following property: If $p$ is prime divisor of $s-t$ , then $p$ divides $a-1$ . Prove that number $\frac{a_{s}-a_{t}}{s-t}$ is an integer.

(FYROM)