Strong Lucas Pseudoprime
المؤلف:
Arnault, F.
المصدر:
"The Rabin-Monier Theorem for Lucas Pseudoprimes." Math. Comput. 66
الجزء والصفحة:
...
25-1-2021
1237
Strong Lucas Pseudoprime
Let 
and 
be Lucas sequences generated by 
and 
, and define
 |
(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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