.svg){kind=logo}
ON RECURRENCE FORMULAS WHICH PRODUCE SQUARE NUMBERS
Keywords:
elliptic threefold, rational point, recurrence formula, sequenceDOI:
https://doi.org/10.17654/0972555525013Abstract
We investigate a problem on squares that are produced by recurrence formulas, and show that the solutions to the problem are parametrized by a certain rational variety. The form of the defining equation enables us to find some periodic solutions, and leads to the study of the group of sections of an elliptic threefold. We show the rank of the group is greater than or equal to two.
Received: January 4, 2025
Accepted: March 7, 2025
References
J. W. S. Cassels, Lectures on elliptic curves, London Math. Soc. Stud. Texts, 24 Cambridge University Press, Cambridge, 1991.
Maplesoft, Maple 2024, Version Maple 2024.1.
The PARI group, PARI/GP, Version 2.15.4. https://pari.math.u-bordeaux.fr/.
J. H. Silverman, Advanced topics in the arithmetic of elliptic curves, Grad. Texts in Math., 151, Springer-Verlag, New York, 1994.
H. Yamagishi, Dynamical systems for figurate numbers and elliptic surfaces, JP Journal of Algebra, Number Theory and Applications 64(1) (2025), 47-79. https://doi.org/10.17654/0972555525004.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
_________________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
