中文

一个与奇完全数相关的指数型丢番图方程

数论 2020-12-29 v2

摘要

我们将证明,对任意给定的素数 17\ell\geq 17p,q1(mod)p, q\equiv 1\pmod{\ell},丢番图方程 (x1)/(x1)=pmq(x^\ell-1)/(x-1)=p^m q 至多有四个正整数解 (x,m)(x, m),并给出其在奇完全数问题上的应用。

关键词

引用

@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}
}

备注

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)