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Fermat's little theorem
If P is a prime number then for any number a, (aP - a) must be divisible by P. This theorem is useful for testing if a number is not prime, though it can't tell if a number is prime. As was his habit, Pierre de Fermat didn't provide a proof (this time saying "I would send you the demonstration, if I did not fear its being too long"). Leonhard Euler first published a proof in 1736, but Gottfried Leibniz left virtually the same proof in an unpublished manuscript from sometime before 1683.
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• MATHEMATICS
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