Arithmetic Progressions in Squarefull Numbers
Number Theory
2023-02-08 v1
Abstract
We answer a number of questions of Erd\H{o}s on the existence of arithmetic progressions in -full numbers (i.e. integers with the property that every prime divisor necessarily occurs to at least the -th power). Further, we deduce a variety of arithmetic constraints upon such progressions, under the assumption of the -conjecture of Masser and Oesterl\'e.
Cite
@article{arxiv.2302.03113,
title = {Arithmetic Progressions in Squarefull Numbers},
author = {Prajeet Bajpai and Michael A. Bennett and Tsz Ho Chan},
journal= {arXiv preprint arXiv:2302.03113},
year = {2023}
}