For 10 points, identify this theorem that states that if p is prime, then for any integer a, a to the quantity p minus one is equivalent to 1, modulo p.
A modified version of this theorem's converse is known as Lehmer's theorem, and a Pratt certificate uses a so-called "witness" in conjunction with Lehmer's theorem. The strict converse of this theorem is disproven by the first set of Knodel numbers, and Euler's totient theorem is a generalization of it. Wilson's theorem is a corollary of it, and it follows almost directly from Lagrange's theorem. Carmichael numbers are counterexamples to this theorem's strict converse, meaning that they are pseudoprime for all integer bases with which they are coprime. For 10 points, identify this theorem that states that if p is prime, then for any integer a, a to the quantity p minus one is equivalent to 1, modulo p.
A modified version of this theorem's converse is known as Lehmer's theorem, and a Pratt certificate uses a so-called "witness" in conjunction with Lehmer's theorem.
Fermat's little theorem