关于 Diophantine 方程 σ2(X¯n) = σn(X¯n)

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-03-26 DOI:10.1142/s1793042124500635

Piotr Miska, Maciej Ulas

引用次数: 0

摘要

在本文中，我们研究了标题 Diophantine 方程的正整数解集 S(n)。特别是，对于给定的 n，我们证明了解的有界性，给出了 σ2(X¯n)和 σn(X¯n)的公共值以及解中出现的变量 xn 的最大值的精确上限。此外，我们列举了 n≤16 的所有解，并讨论了 S(n) 元素上 xn/xn-1 的值集。

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On the Diophantine equation σ2(X¯n) = σn(X¯n)

In this paper, 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 $σ_{2} ({\bar{X}}_{n})$ and $σ_{n} ({\bar{X}}_{n})$ 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 $S (n)$ .

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.