论文标题
在Diophantine方程式上$σ_{2}（\ edimelline {x} _ {n}）=σ_{n}（\ overline {x} _ {n}）$
On the Diophantine equation $σ_{2}(\overline{X}_{n})=σ_{n}(\overline{X}_{n})$
论文作者
论文摘要
在本说明中，我们调查了标题diophantine方程的正整数解决方案的集合$ s（n）$。特别是，对于给定的$ n $，我们证明了解决方案数的有限性，请确切地对$σ_{2}的共同值（\ edline {x} _ {n}）$和$σ_{n} $和$ x {n}（\ edimelline {x}} _ {n}）$以及最大值的$ x_ {此外，我们列举了$ n \ leq 16 $的所有解决方案，并讨论了$ x_ {n}/x_ {n-1} $的值集，而不是$ s（n）$的元素。
In this note we investigate the set $S(n)$ of positive integer solutions of the title Diophantine equation. In particular, for a given $n$ we prove boundedness of the number of solutions, give precise upper bound on the common value of $σ_{2}(\overline{X}_{n})$ and $σ_{n}(\overline{X}_{n})$ together with the biggest value of the variable $x_{n}$ appearing in the solution. Moreover, we enumerate all solutions for $n\leq 16$ and discuss the set of values of $x_{n}/x_{n-1}$ over elements of $S(n)$.
