On the Diophantine equation x2 + bm = cn with a2 + b4 = c2

被引：0

作者：

Terai, Nobuhiro ^{[1
]}

机构：

[1] Oita Univ, Fac Sci & Technol, Dept Integrated Sci & Technol, Div Math Sci, 700 Dannoharu, Oita 8701192, Japan

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2022年 / 53卷 / 01期

关键词：

Diophantine equation; Integer solution; Pythagorean numbers;

D O I：

10.1007/s13226-021-00162-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let a, b, c be pairwise relatively prime positive integers such that a(2) + b(4) = c(2) and b is odd. Then we show that the equation of the title has only one positive integer solution (x, m, n) = (a, 4, 2) under some conditions.

引用

页码：162 / 169

页数：8

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