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Poulet number
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(Definition)
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A Poulet number or Sarrus number is a composite integer $n$ such that $2^n \equiv 2 \mod n$ . In other words, a base 2 pseudoprime (thus a Poulet number that satisfies the congruence for other bases is a Carmichael number). The first few Poulet
numbers are 341, 561, 645, 1105, 1387, 1729, 1905, listed in A001567 of Sloane's OEIS.
For example, 561 is a Poulet number, since $2^{561} - 2$ is 75479248496430827044831091619765377 81833842440832880856752412600491248324784297704172253450355317535082936750061527 689799541169259849585265122868502865392087298790653950 and that's divisible by 561. The number 561 is not prime, it has the prime factors 3, 11, and 17.
Poulet numbers are counterexamples to the Chinese hypothesis.
- 1
- Derrick Henry Lehmer, ``Errata for Poulet's table,'' Math. Comp. 25 25 (1971): 944 - 945.
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"Poulet number" is owned by CompositeFan.
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(view preamble | get metadata)
| Other names: |
Sarrus number |
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Cross-references: Chinese hypothesis, counterexamples, prime factors, prime, number, divisible, OEIS, Carmichael number, bases, congruence, pseudoprime, base, integer, composite
There are 2 references to this entry.
This is version 3 of Poulet number, born on 2008-07-08, modified 2008-07-08.
Object id is 10759, canonical name is PouletNumber.
Accessed 751 times total.
Classification:
| AMS MSC: | 11A51 (Number theory :: Elementary number theory :: Factorization; primality) |
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Pending Errata and Addenda
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