ON THE DIOPHANTINE EQUATION x2

被引：0

作者：

Alan, Murat ^{[1
]}

Aydin, Mustafa ^{[1
]}

机构：

[1] Yildiz Tech Univ, Dept Math, Davutpasa Campus, TR-34210 Istanbul, Esenler, Turkiye

来源：

ARCHIVUM MATHEMATICUM | 2023年 / 59卷 / 05期

关键词：

diophantine equations; primitive divisor theorem; Ramanujan-Nagell equations; X(2)+2(A);

D O I：

10.5817/AM2023-5-411

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we find all integer solutions (x, y, n, a, b, c) of the equation in the title for non-negative integers a, b and c under the condition that the integers x and y are relatively prime and n >= 3. The proof depends on the famous primitive divisor theorem due to Bilu, Hanrot and Voutier and the computational techniques on some elliptic curves.

引用

页码：411 / 420

页数：10

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