## Fermat Quotient

The Fermat quotient for a number and a Prime base is defined as

 (1)

If , then
 (2) (3) (4)

all (mod ). The quantity is known to be Square for only two Primes: the so-called Wieferich Primes 1093 and 3511 (Lehmer 1981, Crandall 1986).

Lehmer, D. H. On Fermat's Quotient, Base Two.'' Math. Comput. 36, 289-290, 1981.