One Integer Point on Some Elliptic Curve to Have Rank 1
Safwan Aouira1, Hasan Sankari2, Ahmad Abdo*3
1Dr. Safwan Aouira, Professor, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
2Dr. Hasan Sankari, Professor, Department of Mathematics, Faculty of Science, Lattakia University, Lattakia, Syria.
3Dr. Ahmad Abdo, Department of Mathematics, Faculty of Science, Aleppo University, Aleppo, Syria.
Manuscript received on 11 April 2026 | First Revised Manuscript received on 19 May 2026 | Second Revised Manuscript received on 03 September 2026 | Manuscript Accepted on 15 October 2026 | Manuscript published on 30 October 2026 | PP: 41-42 | Volume-6 Issue-2, October 2026 | Retrieval Number: 100.1/ijam.A124506010426 | DOI: 10.54105/ijam.A1245.06010426
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© The Authors. Published by Lattice Science Publication (LSP). This is an open-access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Walsh proved a necessary condition for some curves of the form y2 = x3 – px, with p is a prime, to have Mordell – Weil rank 1. In this paper, we extend Walsh’s result to show that some curves have Mordell-Weil rank 1.
Keywords: Elliptic Curves, Integer Points, Rank of Elliptic Curve, Mordell-Weil Rank, and Diophantine Equation.
Scope of the Article: Number Theory