Remark on factorials that are products of factorials

被引：3

作者：

Bhat, K. G. ^{[1
]}

Ramachandra, K. ^{[1
]}

机构：

[1] Indian Inst Sci, Bangalore, Karnataka, India

来源：

MATHEMATICAL NOTES | 2010年 / 88卷 / 3-4期

关键词：

factorial; product of factorials; Stirling's formula; prime factor;

D O I：

10.1134/S0001434610090038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a paper published in 1993, Erdos proved that if n! = a! b!, where 1 < a a parts per thousand currency sign b, then the difference between n and b does not exceed 5 log log n for large enough n. In the present paper, we improve this upper bound to ((1 + epsilon)/ log 2) log log n and generalize it to the equation a (1)!a (2)! ... a (k) ! = n!. In a recent paper, F. Luca proved that n - b = 1 for large enough n provided that the ABC-hypothesis holds.

引用

页码：317 / 320

页数：4