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Euler-Lucas Pseudoprime

Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define

D=P^2-4Q.
(1)

Then

{U_((n-(D/n))/2)=0 (mod n) when (Q/n)=1; V_((n-(D/n))/2)=D (mod n) when (Q/n)=-1,
(2)

where (Q/n) is the Legendre symbol. An odd composite number n such that (n,QD)=1 (i.e., n and QD are relatively prime) is called an Euler-Lucas pseudoprime with parameters (P,Q).

See also

Pseudoprime, Strong Lucas Pseudoprime

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References

Ribenboim, P. "Euler-Lucas Pseudoprimes (elpsp(P,Q)) and Strong Lucas Pseudoprimes (slpsp(P,Q))." §2.X.C in The New Book of Prime Number Records. New York: Springer-Verlag, pp. 130-131, 1996.

Referenced on Wolfram|Alpha

Euler-Lucas Pseudoprime

Cite this as:

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

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