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.

elliptic threefold, rational point, recurrence formula, sequence.

Received: January 4, 2025; Accepted: March 7, 2025; Published: March 21, 2025

How to cite this article: Hizuru Yamagishi, On recurrence formulas which produce square numbers, JP Journal of Algebra, Number Theory and Applications 64(3) (2025), 221-238. https://doi.org/10.17654/0972555525013

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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