Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 83-87.

A QUESTION OF ERDŐS ON 3-POWERFUL NUMBERS AND AN ELLIPTIC CURVE ANALOGUE OF THE ANKENY-ARTIN-CHOWLA CONJECTURE

P. G. Walsh

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 Erdős on 3-powerful numbers, and state a related conjecture which can be viewed as an elliptic curve analogue of the famous Ankeny-Artin-Chowla conjecture.

2020 Mathematics Subject Classification.   11D25, 11G05.

Key words and phrases.   Powerful number, diophantine equation, elliptic curve.

DOI: https://doi.org/10.21857/y7v64t4jky

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