If $a$ and $b$ are distinct integers, prove that $a-b$ is a factor of $a^n-b^n$, whenever $n$ is a positive integer.

When n is an even number then $a^n-b^n$ can be written as $(a^{n/2}-b^{n/2})(a^{n/2}+b^{n/2})$. here if $\frac{n}{2}$ is even then it can be further expanded and finally we will get (a-b)*(some thing).