Friday, 5 December 2014

number theory - How can I prove divisibility using congruence?

I'm new to this, so please excuse me if I said something wrong or offended anyone.
We're doing the number theory in class, and I came across this question, which I had no idea how to even begin..:



Use congruences to prove 5|(n5 − n)
(by the way, we already proved this using induction)



Does anyone know how to do this?
Thank you so much in advance.

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