A number satisfies the Carmichael condition Iff for all Prime Divisors of . This is equivalent to the condition for all Prime Divisors of .
See also Carmichael Number
Borwein, D.; Borwein, J. M.; Borwein, P. B.; and Girgensohn, R. ``Giuga's Conjecture on Primality.''
Amer. Math. Monthly 103, 40-50, 1996.