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

(1) |

(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).

**References**

Crandall, R. *Projects in Scientific Computation.* New York: Springer-Verlag, 1986.

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

© 1996-9

1999-05-26