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arXiv · 2404.03970

A question of Erd\"{o}s on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture

P. G. Walsh
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Abstract

We describe how the Mordell-Weil group of rational points on a certain family of elliptic curves give rise to solutions to a conjecture of Erd\"{o}s on $3$-powerful numbers, and state a related conjecture which can be viewed as an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture.

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P. G. Walsh. 2024-04-05. A question of Erd\"{o}s on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture. https://arxiv.org/abs/2404.03970

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