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arXiv · 2302.03113

Arithmetic Progressions in Squarefull Numbers

Prajeet Bajpai·Michael A. Bennett·Tsz Ho Chan
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Abstract

We answer a number of questions of Erd\H{o}s on the existence of arithmetic progressions in $k$-full numbers (i.e. integers with the property that every prime divisor necessarily occurs to at least the $k$-th power). Further, we deduce a variety of arithmetic constraints upon such progressions, under the assumption of the $abc$-conjecture of Masser and Oesterl\'e.

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Prajeet Bajpai, Michael A. Bennett, Tsz Ho Chan. 2023-02-06. Arithmetic Progressions in Squarefull Numbers. https://arxiv.org/abs/2302.03113

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