Almost squares and factorisations in consecutive integers

被引：31

作者：

Saradha, N ^{[1
]}

Shorey, TN ^{[1
]}

机构：

[1] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

来源：

COMPOSITIO MATHEMATICA | 2003年 / 138卷 / 01期

关键词：

consecutive; diophantine equations; elliptic equations; factorisation; primes;

D O I：

10.1023/A:1025480729778

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that there is no square other than 12(2) and 720(2) such that it can be written as a product of k - 1 integers out of k (greater than or equal to3) consecutive positive integers. We give an extension of a theorem of Sylvester that a product of k consecutive integers each greater than k is divisible by a prime exceeding k.

引用

页码：113 / 124

页数：12

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