ODD PERFECT NUMBERS, DIOPHANTINE EQUATIONS, AND UPPER BOUNDS

被引：17

作者：

Nielsen, Pace P. ^{[1
]}

机构：

[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA

来源：

MATHEMATICS OF COMPUTATION | 2015年 / 84卷 / 295期

关键词：

Diophantine equation; perfect number; LARGEST PRIME DIVISOR;

D O I：

10.1090/S0025-5718-2015-02941-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a new upper bound for odd multiperfect numbers. If N is an odd perfect number with k distinct prime divisors and P is its largest prime divisor, we find as a corollary that 10(12)P(2)N < 2(4k). Using this new bound, and extensive computations, we derive the inequality k >= 10.

引用

页码：2549 / 2567

页数：19

共 16 条

[1]

BRENT RP, 1991, MATH COMPUT, V57, P857, DOI 10.1090/S0025-5718-1991-1094940-3

[2]

CHEIN JEZ, 1979, THESIS PENNSYLVANIA

[3] IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS [J].