my favorite proof of fermat's little theorem

necklaces :D

my favorite proof of fermat's little theorem my favorite proof of fermat's little theorem APR 15, 2026 inkhaven One of the first things you learn when you learn in elementary number theory is Fermat's Little Theorem (so named to differentiate it from the big bad Last Theorem). Theorem. (Fermat's Little Theorem) Let p p p be a prime number and a a a be an integer. Then a p ≡ a ( m o d p ) . a^{p}\equiv a \pmod p. a p ≡ a ( mod p ) . There are many proofs of this theorem, but my favorite one is a combinatorial proof that goes by counting necklaces. Suppose you have a a a different colored beads.

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• Gloria Ma

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