On the Diophantine system f (z) = f (x) f (y) = f (u) f (v)

被引：0

作者：

Zhang, Yong ^{[1
]}

Shen, Zhongyan ^{[2
]}

机构：

[1] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China

[2] Zhejiang Int Studies Univ, Dept Math, Hangzhou 310012, Zhejiang, Peoples R China

来源：

PERIODICA MATHEMATICA HUNGARICA | 2017年 / 75卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Diophantine system; Positive integer solution; Rational solution; Elliptic curve; EQUATION (X(K)-1)(Y(K)-1); PRODUCTS;

D O I：

10.1007/s10998-017-0198-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that the Diophantine system f (z) = f (x) f (y) = f (u) f (v) has infinitely many nontrivial positive integer solutions for f (X) = X-2 - 1, and infinitely many nontrivial rational solutions for f (X) = X-2 + b with nonzero integer b.

引用

页码：295 / 301

页数：7

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