ODD PERFECT NUMBERS, DIOPHANTINE EQUATIONS, AND UPPER BOUNDS

被引：16
|
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.
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页码：2549 / 2567
页数：19
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