A conjecture concerning the pure exponential diophantine equation ax + by = cz

被引：9

作者：

Le, MH ^{[1
]}

机构：

[1] Zhanjiang Normal Coll, Dept Math, Zhanjiang 524005, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2005年 / 21卷 / 04期

基金：

中国国家自然科学基金;

关键词：

pure exponential diophantine equation; number of solutions; completely determine;

D O I：

10.1007/s10114-004-0436-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let a, b, c, r be fixed positive integers such that a(2) + b(2) = c(r), min(a, b, c, r) > 1 and 2 inverted iota r. In this paper we prove that if a equivalent to 2 (mod 4), b equivalent to 3 (mod 4), c > 3. 10(37) and r > 7200, then the equation a(x) + b(y) = c(z) only has the solution (x, y, z) = (2, 2, r).

引用

页码：943 / 948

页数：6

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