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单词 Poulet Number
释义

Poulet Number

A Fermat Pseudoprime to base 2, denoted psp(2), i.e., a Composite Odd Integer such that


The first few Poulet numbers are 341, 561, 645, 1105, 1387, ... (Sloane's A001567). Pomerance et al. (1980) computed all21,853 Poulet numbers less than .


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.

See also Fermat Pseudoprime, Pseudoprime, Super-Poulet Number


References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 28-29, 1994.

Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. ``The Pseudoprimes to .'' Math. Comput. 35, 1003-1026, 1980. Available electronically from ftp://sable.ox.ac.uk/pub/math/primes/ps2.Z.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 115-117, 1993.

Sloane, N. J. A. SequenceA001567/M5441in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.


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