Fermat's little theorem has been the basis of many primality testing
algorithms. However the major problem with these test has been the existence
of Carmichael Numbers. In this report we have tried to extend the Fermat's
test to bigger fields and we encountered numbers similar to Carmichael
Numbers. These numbers have been named as Genreralized Carmichael Numbers.
We have identified the exact criterion for Generalized carmichael Numbers,
some interesting properties of them and a lower bound on number of Generalized
Carmichaels less than x. Finally, the lower bound, when combined with two
well-known conjuctures of Number Theory, suggests there are infinitely
many Generalized Carmichael Numbers.
Full Report (PS-gzipped: 122K)