Squarefree smooth numbers and Euclidean prime generators
Number Theory
2017-04-11 v4
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.
Cite
@article{arxiv.1607.01557,
title = {Squarefree smooth numbers and Euclidean prime generators},
author = {Andrew R. Booker and Carl Pomerance},
journal= {arXiv preprint arXiv:1607.01557},
year = {2017}
}
Comments
8 pages, to appear in Proceedings of the AMS