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arXiv · 2410.23240

A note on non-integrality of the $(k,l)$-G\"{o}bel sequences

Yuh Kobayashi·Shin-ichiro Seki
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Abstract

The $(k,l)$-G\"{o}bel sequences defined by Ibstedt remain integers for the first (in some cases, many) terms, but for selected values of $(k,l)$, computations show that the terms eventually stop being integers. It is still unresolved whether the integrality of these sequences breaks down for all $k, l\geq 2$. In this article, we prove the non-integrality for a specific class of $(k,l)$ values. Our proof is based on geometric arguments related to the distribution of quadratic residues modulo a prime.

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Yuh Kobayashi, Shin-ichiro Seki. 2024-10-30. A note on non-integrality of the $(k,l)$-G\"{o}bel sequences. https://arxiv.org/abs/2410.23240

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