Exceptional cases of Terai’s conjecture on Diophantine equations

被引：0
|
作者：
Takafumi Miyazaki
机构：
[1] Tokyo Metropolitan University,Department of Mathematics and Information Sciences
来源：
Archiv der Mathematik | 2010年 / 95卷
关键词：
Primary 11D61; Secondary 11A07; Exponential Diophantine equations; Terai’s conjecture;
D O I：
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学科分类号：
摘要：
Let a, b, c be relatively prime positive integers such that ap + bq = cr for fixed integers p, q, r ≥ 2. Terai conjectured that the equation ax + by = cz in positive integers has only the solution (x, y, z) = (p, q, r) except for specific cases. In this paper, we consider the case q = r = 2 and give some results related to exceptional cases.
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页码：519 / 527
页数：8
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