Thread: Converse of Fermat's Little Theorem (particular case)

Let with such that and are all prime numbers.

Show that (mod n) whenever hcf (a,n) = 1.

Carmichael Number -- from Wolfram MathWorld

Let be of the following form:



If each factor is prime, then for all . By Korselt's criteria, this property makes n a Carmichael Number, which by definition, is any composite number that passes Fermat's test.