Poulet Number
المؤلف:
Guy, R. K.
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
25-1-2021
975
Poulet Number
A Poulet number is a Fermat pseudoprime to base 2, denoted psp(2), i.e., a composite number 
such that
The first few Poulet numbers are 341, 561, 645, 1105, 1387, ... (OEIS A001567).
Pomerance et al. (1980) computed all 
Poulet numbers less than 
. The numbers less than 
, 
, ..., are 0, 3, 22, 78, 245, ... (OEIS A055550).
Pomerance has shown that the number of Poulet numbers less than 
for sufficiently large 
satisfy
(Guy 1994).
A Poulet number all of whose divisors 
satisfy 
is called a super-Poulet number. There are an infinite number of Poulet numbers which are not super-Poulet numbers. Shanks (1993) calls any integer satisfying 
(i.e., not limited to odd composite numbers) a Fermatian.
REFERENCES:
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 28-29, 1994.
Pinch, R. G. E. "The Pseudoprimes Up to 
." ftp://ftp.dpmms.cam.ac.uk/pub/PSP/.
Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. "The Pseudoprimes to 
." Math. Comput. 35, 1003-1026, 1980. http://mpqs.free.fr/ThePseudoprimesTo25e9.pdf.
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 115-117, 1993.
Sloane, N. J. A. Sequences A001567/M5441 and A055550 in "The On-Line Encyclopedia of Integer Sequences."
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