I need to prove by induction if ${n^5 - n}$ is divisible by 5 and I have no idea how I would do it.
I am trying to prove it for several hours now, I started with ${n^5 - n} \mod 5 = 0$ but then I realized that I have no idea how to use modulo for transformations.
The next thing I tried was $(5 + n)\frac{n^5 - n}5 = \frac{(n+1)^5 - n+1}5$ but it didn't get me anywhere.
How would you do it?