塞尔弗里奇问题的一个推广
A generalization of Selfridge's question
摘要：
塞尔弗里奇要求调查对$(m,n)$的自然数，其中$2^m - 2^n$除$x^m - x^n$的所有整数$x.$这个问题是由不同的数学家回答表明，只有100多个这样的对。设$R$是数域$\K$的整数环，$M_n(R)$是$R$上所有$n \times n$矩阵的环.在这篇文章中，我们证明了一个推广的塞尔弗里奇的问题的情况下，$M_n(R)$。
英文摘要：
Selfridge asked to investigate the pairs $(m,n)$ of natural numbers for which $2^m - 2^n$ divides $x^m - x^n$ for all integers $x.$ This question was answered by different mathematicians by showing that there are only finitely many such pairs. Let $R$ be the ring of integers of a number field $\K$ and $M_n(R)$ be ring of all $n \times n$ matrices over $R$. In this article, we prove a generalization of Selfridge's question in the case of $M_n(R)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
