Proof that $a^p-a$ is divisible by $p$ where $p$ is a prime number?

Question

What is a proof that $a^p-a$ is divisible by $p$ where $p$ is a prime number?

https://en.wikipedia.org/wiki/Fermat%27s_little_theorem – Dhanvi Sreenivasan May 04 '20 at 07:28 — Dhanvi Sreenivasan, May 04 '20 at 07:28

score 0 · Answer 1 · answered May 04 '20 at 07:28

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This is Fermat little theorem. You can prove it by using Binomial theorem and/or induction.

Also you can find it here:https://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem

answered May 04 '20 at 07:28

nonuser

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Just commented :P – Dhanvi Sreenivasan May 04 '20 at 07:28

score 0 · Answer 2 · answered May 04 '20 at 07:32

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It's indeed lil' Fermat. I like the group theory proof best, probably. Though that proof may be over your head at this point. Let me know if you want to see it.

answered May 04 '20 at 07:32

Proof that $a^p-a$ is divisible by $p$ where $p$ is a prime number?

2 Answers2