The Fermat quotient for a number a and a prime base p is defined as q_p(a) congruent (a^(p - 1) - 1)/p. If p not vertical bar a b, then q_p(a b) | = | q_p(a) + q_p(b) q_p(p ± 1) | = | ∓ 1 (mod p), where the modulus is taken as a fractional congruence.