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arXiv · 2503.21485

A note on three consecutive powerful numbers

Tsz Ho Chan
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Abstract

This note concerns the non-existence of three consecutive powerful numbers. We use Pell equations, elliptic curves, and second-order recurrences to show that there are no such triplets with the middle term a perfect cube and each of the other two having only a single prime factor raised to an odd power.

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Tsz Ho Chan. 2025-03-27. A note on three consecutive powerful numbers. https://arxiv.org/abs/2503.21485

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