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Date: 18-4-2020
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Date: 18-10-2019
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Date: 12-1-2021
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Let and
be Lucas sequences generated by
and
, and define
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(1) |
Let be an odd composite number with
, and
with
odd and
, where
is the Legendre symbol. If
![]() |
(2) |
or
![]() |
(3) |
for some with
, then
is called a strong Lucas pseudoprime with parameters
.
A strong Lucas 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 twin primes 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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