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Squarefree smooth numbers and Euclidean prime generators


Authors: Andrew R. Booker and Carl Pomerance
Journal: Proc. Amer. Math. Soc. 145 (2017), 5035-5042
MSC (2010): Primary 11A41; Secondary 11A15, 11B25, 11L40
DOI: https://doi.org/10.1090/proc/13576
Published electronically: August 31, 2017
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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.


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Additional Information

Andrew R. Booker
Affiliation: School of Mathematics, Bristol University, University Walk, Bristol, BS8 1TW, United Kingdom
Email: andrew.booker@bristol.ac.uk

Carl Pomerance
Affiliation: Mathematics Department, Dartmouth College, Hanover, New Hampshire 03755
Email: carl.pomerance@dartmouth.edu

DOI: https://doi.org/10.1090/proc/13576
Received by editor(s): July 6, 2016
Received by editor(s) in revised form: July 7, 2016, and November 4, 2016
Published electronically: August 31, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society

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