# Poulet number

A Poulet number^{} or Sarrus number is a composite integer $n$ such that ${2}^{n}\equiv 2modn$. 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^{}.

## References

- 1 Derrick Henry Lehmer, “Errata for Poulet’s table,” Math. Comp. 25 25 (1971): 944 - 945.

Title | Poulet number |
---|---|

Canonical name | PouletNumber |

Date of creation | 2013-03-22 18:11:12 |

Last modified on | 2013-03-22 18:11:12 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 6 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A51 |

Synonym | Sarrus number |