Consider a Lucas sequence with P>0 and Q = ± 1. A Fibonacci pseudoprime is a composite number n such that V_n congruent P (mod n). There exist no even Fibonacci pseudoprimes with parameters P = 1 and Q = - 1 (Di Porto 1993) or P = Q = 1. André-Jeannin also proved that if (P, Q)!=(1, -1) and (P, Q)!=(1, 1), then there exists at least one even Fibonacci pseudoprime with parameters P and Q.

pseudoprime

Leonardo Fibonacci