完美数及其相关问题  

Perfect Numbers and the Related Problems

作　　者：蔡天新[1] Tyler ROSS CAI Tianxin;Tyler ROSS(School of Mathematical Sciences,Zhejiang University,Hangzhou,Zhejiang,310058,P.R.China)

机构地区：[1]浙江大学数学科学学院,杭州浙江310058

出　　处：《数学进展》2024年第4期673-689,共17页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.12071421)。

摘　　要：完美数问题是最古老的数学问题之一,可能来源于古希腊的毕达哥拉斯学派,被意大利当代数学家奥迪弗雷迪列为面向21世纪的“四大数学难题”之首.本文对古老的完美数问题及相关的梅森素数进行综述,尤其是对其拓展为平方完美数、立方完美数及S-完美数以后所产生的问题进行了综述.The perfect number problem is one of the oldest mathematical problems,possibly originating from the Pythagorean school in ancient Greece.It was listed by contemporary Italian mathematician P.G.Odifreddi as the top of the"Four Mathematical Difficulties"facing the 21st century.This article is a survey of the ancient problem of perfect numbers and the related Mersenne prime numbers,especially the problems that arise after generalizing them to square perfect numbers,cubic perfect numbers,and S-perfect numbers.

关 键 词：完美数 平方完美数 立方完美数 S-完美数 

分 类 号：O156[理学—数学]