Almost squares in arithmetic progression

被引：21

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：

arithmetic progressions; congruences; diophantine equations; elliptic equations; Legendre symbol; squarefree integers; PERFECT POWERS; PRODUCTS; TERMS;

D O I：

10.1023/A:1025408727362

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that a product of four or more terms of positive integers in arithmetic progression with common difference a prime power is never a square. More general results are given which completely solve (1.1) with gcd(n, d) = k greater than or equal to 3 and 1 < d <= 104.

引用

页码：73 / 111

页数：39

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