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Fibonacci Pseudoprime


Consider a Lucas sequence with P>0 and Q=+/-1. A Fibonacci pseudoprime is a composite number n such that

 V_n=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 1996). André-Jeannin (1996) 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.


See also

Pseudoprime

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References

André-Jeannin, R. "On the Existence of Even Fibonacci Pseudoprimes with Parameters P and Q." 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.

Referenced on Wolfram|Alpha

Fibonacci Pseudoprime

Cite this as:

Weisstein, Eric W. "Fibonacci Pseudoprime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FibonacciPseudoprime.html

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