## Prove

Sudip Deb new
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### Prove

Prove that (n^5 - n) is divided by 5 .

HandaramTheGreat
Posts: 135
Joined: Thu Dec 09, 2010 12:10 pm

### Re: Prove

if you put 2 dollar sign in both side of (n^5-n), it would be like this $(n^5-n)$...

Moon
Also you can always use Fermat's Little Theorem, which states that for all $n\in\mathbb{N}$ and any prime $p$ $n^p \equiv n \pmod{p}$
When $gcd(n,p)=1$, you can divide the equivalence by $n$ and get $n^{p-1} \equiv 1 \pmod{p}$.