Vandiver's Criteria

Let  be an irregular prime, and let  be a prime with . Also let  be an integer such that  (mod ). For an irregular pair , form the product

(1)

where

			(2)
			(3)

If  (mod ) for all such irregular pairs, then Fermat's last theorem holds for exponent .

REFERENCES:

Johnson, W. "Irregular Primes and Cyclotomic Invariants." Math. Comput. 29, 113-120, 1975.