Let with such that and are all prime numbers.

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

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- Apr 30th 2009, 10:16 AMAmanda1990Converse 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. - Apr 30th 2009, 01:02 PMMedia_ManCarmichael Numbers
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.