Squarefree smooth numbers and Euclidean prime generators

Andrew R. Booker; Carl Pomerance

doi:10.1090/proc/13576

Squarefree smooth numbers and Euclidean prime generators

Andrew R. Booker, Carl Pomerance

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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
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	https://doi.org/10.1090/proc/13576
Publication status	Published - 1 Dec 2017

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via AMS at http://www.ams.org/journals/proc/0000-000-00/S0002-9939-2017-13576-X/home.html. Please refer to any applicable terms of use of the publisher.
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Squarefree smooth numbers and Euclidean prime generators

Abstract

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