A note on three consecutive powerful numbers
Number Theory
2025-03-28 v1
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.
Cite
@article{arxiv.2503.21485,
title = {A note on three consecutive powerful numbers},
author = {Tsz Ho Chan},
journal= {arXiv preprint arXiv:2503.21485},
year = {2025}
}
Comments
7 pages