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arXiv · 1802.09195

An exponential diophantine equation related to odd perfect numbers

Tomohiro Yamada
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Abstract

We shall show that, for any given primes $\ell\geq 17$ and $p, q\equiv 1\pmod{\ell}$, the diophantine equation $(x^\ell-1)/(x-1)=p^m q$ has at most four positive integral solutions $(x, m)$ and give its application to odd perfect number problem.

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Tomohiro Yamada. 2018-02-26. An exponential diophantine equation related to odd perfect numbers. https://arxiv.org/abs/1802.09195

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