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).
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页码：943 / 948
页数：6
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