P-adic Valuation of Difference of Powers with Coprime Exponent

Theorem
Let $x, y \in \Z$ be distinct integers.

Let $n \ge 1$ be a natural number.

Let $p$ be a prime number.

Let:
 * $p \divides x - y$

and:
 * $p \nmid x y n$.

Then
 * $\map {\nu_p} {x^n - y^n} = \map {\nu_p} {x - y}$

where $\nu_p$ denotes $p$-adic valuation.

Also see

 * Lifting The Exponent Lemma