发表机构
Federal Rural University of Pernambuco (UFRPE)（伯南布哥联邦农村大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究同余方程$\binom{2n}{n}\boldsymbol{\text{≡}}2^n \bmod n$的解，借助SageMath软件及自身结果增加了已知解的数量，还证明了偶完全数、Wieferich素数与该方程解的关联。
AI 中文摘要
本文聚焦同余方程$\binom{2n}{n}\boldsymbol{\text{≡}}2^n \bmod n$的解，利用本文的主要结果与SageMath软件，大幅增加了已知解的数量，还证明了偶完全数、Wieferich素数等著名数与该方程的解存在关联。
英文摘要
In this article we focus on the solutions of a congruence equation: $\binom{2n}{n}\equiv 2^n \bmod n$. Using the main result of this article and the SageMath software, we improve largely the number of known solutions. Furthermore, we prove that some famous numbers like even perfect numbers and Wieferich primes are connected to solutions of this equation.
Comments8 pages, 1 table. Published version
Journal refNotes on Number Theory and Discrete Mathematics 29 (2023), no. 4, 705-712
DOI：10.7546/nntdm.2023.29.4.705-712
