On Terai's conjecture

被引：12

作者：

Cao, ZF ^{[1
]}

Dong, SL ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 1998年 / 74卷 / 08期

关键词：

D O I：

10.3792/pjaa.74.127

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Terai presented the following conjecture:If a(2) + b(2) = c(2) with a > 0, b > 0, c > 0, gcd (a, b, c) = 1 and a even, then the diophantine equation x(2) + b(m) = c(n) has the only positive integral solution (x, m, n) = (a, 2, 2). In this paper we prove that if (i) b is a prime power, c = 5 (mod 8), or (ii) c = 5 (mod 8) is a prime power, then Terai's conjecture holds.

引用

页码：127 / 129

页数：3

共 17 条

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