An extension of Aigner's theorem

被引：0

作者：

Tho, Nguyen Xuan ^{[1
]}

机构：

[1] Hanoi Univ Sci & Technol, Hanoi, Vietnam

来源：

MONATSHEFTE FUR MATHEMATIK | 2024年 / 204卷 / 01期

关键词：

Diophantine equations; Fermat equations; Algebraic number fields; Rational function fields; FERMATS LAST THEOREM; TERNARY DIOPHANTINE EQUATIONS; ALGEBRAIC POINTS; CLASS FIELDS;

D O I：

10.1007/s00605-023-01913-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1957, Aigner (Monatsh Math 61:147-150, 1957) showed that the equations x(6) + y(6) = z(6) and x(9) + y(9) = z(9) have no solutions in any quadratic number field with xyz not equal 0. We show that Aigner's result holds for all equations x(3n) + y(3n) = z(3n), where n >= 2 is a positive integer. The proof combines Aigner's idea with deep results on Fermat's equation and its variants.

引用

页码：191 / 195

页数：5

共 33 条

[1]

Aigner A., 1934, JAHRESBER DTSCH MATH, V43, P226

[2]

Aigner A., 1957, Monatsh. Math., V61, P147

[3] Ternary Diophantine equations of signature (p, p, 3) [J].