纺织高校基础科学学报2017，Vol.30Issue(3)：302-304,310,4.DOI:10.13338/j.issn.1006-8341.2017.03.002
关于数论函数方程σ(x3)=y2的一点注记
A note on the arithmetic functional equation σ (x3) =y2
摘要
Abstract
For any positive integer a,let σ(a) denote the sum of all divisors of a.Let p be an odd prime,and let r,s be positive integers.It is proved that the equation σ (x3) =y2 has no positive integer solution (x,y) such that x=2rps and one of the following condition is satisfied:(i) 2(|)r,p≡1 (mod 6).(ii) 2(|)r,p≡5 (mod 6) and 2(|)s.(iii) 2(|)rs,p is a Fermat prime.关键词
约数和/数论函数方程/平方数Key words
sum of divisors/arithmetic functional equation/square分类
数理科学引用本文复制引用
潘晓玮..关于数论函数方程σ(x3)=y2的一点注记[J].纺织高校基础科学学报,2017,30(3):302-304,310,4.基金项目
国家自然科学基金资助项目(11526162) （11526162）
陕西省自然科学基金资助项目(2016JQ1040) （2016JQ1040）
