On the Diophantine equation X4

被引：0

作者：

Alavi, S. D. ^{[1
]}

Janfada, A. S. ^{[1
]}

Abbaspour, A. ^{[1
]}

机构：

[1] Urmia Univ, Dept Math, Orumiyeh 5756151818, Iran

来源：

ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2019年 / 42期

关键词：

diophantine equation; elliptic curve;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

First we prove that, under a certain condition, the Diophantine equation X-4 + hY(3) = Z(4) + hW(3), where h is a rational number, has infinitely many nontrivial integral solutions. Using this result we deduce that, under a condition, for k >= 2, the Diophantine equation X-4+Y-1(3) +Y-2(3) + . . . +Y-k(3) = Z(4)+W-1(3) +W-2(3) + . . . +W-k(3) has infinitely many nontrivial integral solutions. Then, we conjecture, by some evidences, that the above conditions may be removed.

引用

页码：324 / 329

页数：6

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