prove that [n^5 - n] is divisible by 30 for n >= 3

Hey all!
I need to prove that 30 is a divisor of \(\displaystyle n^5-n\) for \(\displaystyle n\ge3\).

I tried expanding:

\(\displaystyle n^5-n=n(n^4-1)=n(n^2+1)(n^2-1)=n(n^2+1)(n+1)(n-1)\).

But this doesn't seem to help.

Please help!

Re: prove [n^5-n] divides by 30

See here:

http://mathforum.org/library/drmath/view/60840.html

Re: prove [n^5-n] divides by 30

Thanks a lot for the link!

galactus said:

See here:

http://mathforum.org/library/drmath/view/60840.html

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