n=2^（alpha）*5^（beta）的Subbarao同余式的一个变式
A variation of a congruence of Subbarao for n=2^(alpha)*5^(beta)
摘要：
关于满足某些同余的正整数$n$的特征，以及正整数$n$的欧拉函数$φ$和正因子和函数$σ$，有许多公开的问题。本文讨论了$$ nφ(n)\equiv2\pmod{σ(n)} $$形式的同余关系，证明了满足上述同余关系的$2^α5^β, \enspace α, β\geq0,$形式的正整数只有$n=1, 2, 5, 8$ .
英文摘要：
There are many open problems concerning the characterization of the positive integers $n$ fulfilling certain congruences and involving the Euler totient function $φ$ and the sum of positive divisors function $σ$ of the positive integer $n$. In this work, we deal with the congruence of the form $$ nφ(n)\equiv2\pmod{σ(n)} $$ and we prove that the only positive integers of the form $2^α5^β, \enspace α, β\geq0,$ that satisfy the above congruence are $n=1, 2, 5, 8$.
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。
