### Abstract

We show that for each prime

*p*> 7, every residue mod*p*can be represented by a squarefree number with largest prime factor at most*p*. We give two applications to recursive prime generators akin to the one Euclid used to prove the infinitude of primes.Original language | English |
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Pages (from-to) | 5035-5042 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 12 |

Early online date | 31 Aug 2017 |

DOIs | |

Publication status | Published - 1 Dec 2017 |

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## Cite this

Booker, A. R., & Pomerance, C. (2017). Squarefree smooth numbers and Euclidean prime generators.

*Proceedings of the American Mathematical Society*,*145*(12), 5035-5042. https://doi.org/10.1090/proc/13576