Objects that violate the converse of this theorem can be detected via Korselt's criterion. The exponent in this theorem is replaced with “phi-of-n” to extend it to arbitrary integers in Euler's theorem. This theorem can be proved combinatorially by counting necklaces whose beads must not all be the same color, or algebraically by applying Lagrange's theorem to (*) Z-sub-p. This theorem and its generalizations are used to prove the correctness of RSA. Since the Carmichael numbers are never detected as composite by a test based on this theorem, they are called pseudoprimes. This theorem published in 1640 states that, for all a and prime p, “a to the p is equivalent to a mod p.” For 10 points, name this theorem in number theory by a French mathematician who also names a “last” theorem. ■END■
ANSWER: Fermat’s little theorem [prompt on Fermat’s theorem; reject “Fermat’s last theorem”]
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= Average correct buzz position