An exponential diophantine equation related to odd perfect numbers

Tomohiro Yamada

An exponential diophantine equation related to odd perfect numbers

Number Theory 2020-12-29 v2

Authors: Tomohiro Yamada

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.

Keywords

exponential diophantine equation odd perfect numbers prime numbers integral solutions

Cite

@article{arxiv.1802.09195,
  title  = {An exponential diophantine equation related to odd perfect numbers},
  author = {Tomohiro Yamada},
  journal= {arXiv preprint arXiv:1802.09195},
  year   = {2020}
}

Comments

11 pages, filled some gaps and constants changed due to correction of our old paper in Colloq. Math. 156 (2019), 15--23. (see ibid. 162 (2019), 311--313)

An exponential diophantine equation related to odd perfect numbers

Abstract

Keywords

Cite

Comments

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