MATH PUZZLE OF THE DAY More number theory! 1) Prove that if p is prime, 2^p = 2 mod p 2) Find a nonprime for which that is also true.
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Well then prove Fermat’s little theorem if you have to! Here’s a hint: polynomials of degree n have at most n roots, in a field. The difference between primes and non-primes is that the integers modulo a prime form a field.
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Actually, it’s even easier than that. The non-zero residue classes mod p form a group of order p-1 under multiplication, and the equation x^|G|=1 is universally true in all finite groups. Fermat’s Little Theorem follows immediately.
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