Strong Lucas Pseudoprime
Let 
and 
be Lucas Sequences generated by 
and 
, and define
Let
be an Odd Composite Number with 
, and 
with 
Odd and 
, where
is the Legendre Symbol. If
or
for some
with 
, then is called a strong Lucas pseudoprime with parameters 
. A strongLucas pseudoprime is a Lucas Pseudoprime to the same base. Arnault (1997) showed that any Composite Number is a strong Lucas pseudoprime for at most 4/15 of possible bases (unless is the Product of TwinPrimes having certain properties).
References
Arnault, F. ``The Rabin-Monier Theorem for Lucas Pseudoprimes.'' Math. Comput. 66, 869-881, 1997. Ribenboim, P. ``Euler-Lucas Pseudoprimes (elpsp(
)) and Strong Lucas Pseudoprimes (slpsp()).'' §2.X.C in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 130-131, 1996.
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