On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function
Year: 2025
Type: preprint
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 $0.73194$.
Source: arXiv (Cornell University)
Author: Yamada, Tomohiro
Institution: The University of Osaka
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7091186546
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