FACTORIALS AND THE RAMANUJAN FUNCTION

被引：2

作者：

Bravo, Jhon J. ^{[1
]}

Luca, Florian ^{[2
]}

机构：

[1] Univ Cauca, Dept Matemat, Calle 5 4-70, Popayan, Colombia

[2] Univ Witwatersrand, Sch Math, Private Bag 3, ZA-2050 Johannesburg, Johannesburg, South Africa

来源：

GLASGOW MATHEMATICAL JOURNAL | 2016年 / 58卷 / 01期

关键词：

LEHMER-NUMBERS; DIVISORS; LUCAS;

D O I：

10.1017/S0017089515000130

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 2006, F. Luca and I. E. Shparlinski (Proc. Indian Acad. Sci. (Math. Sci.) 116(1) (2006), 1-8) proved that there are only finitelymany pairs (n, m) of positive integers which satisfy the Diophantine equation vertical bar tau (n!)vertical bar = m!, where tau is the Ramanujan function. In this paper, we follow the same approach of Luca and Shparlinski (Proc. Indian Acad. Sci. (Math. Sci.) 116(1) (2006), 1-8) to determine all solutions of the above equation. The proof of our main theorem uses linear forms in two logarithms and arithmetic properties of the Ramanujan function.

引用

页码：177 / 185

页数：9

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