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.
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页码：191 / 195
页数：5
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