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arXiv · 2510.11252

On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function

Tomohiro Yamada
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Abstract

We prove that the sum of reciprocals $1/x$ of integer solutions of $(x^m-1)/(x-1)=N$ with $x, m\geq 2$ for a given integer $N$ except the smallest $x$ is smaller than $5.9037$. If we limit $x$ to be prime, then the sum is smaller than $0.73194$.

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Tomohiro Yamada. 2025-10-13. On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function. https://arxiv.org/abs/2510.11252

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