Fibonacci Pseudoprime

Consider a Lucas sequence with  and . A Fibonacci pseudoprime is a composite number  such that

There exist no even Fibonacci pseudoprimes with parameters  and  (Di Porto 1993) or  (André-Jeannin 1996). André-Jeannin (1996) also proved that if  and , then there exists at least one even Fibonacci pseudoprime with parameters  and .

REFERENCES:

André-Jeannin, R. "On the Existence of Even Fibonacci Pseudoprimes with Parameters  and ." Fib. Quart. 34, 75-78, 1996.

Di Porto, A. "Nonexistence of Even Fibonacci Pseudoprimes of the First Kind." Fib. Quart. 31, 173-177, 1993.

Ribenboim, P. "Fibonacci Pseudoprimes." §2.X.A in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 127-129, 1996.