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
收藏
页码：295 / 301
页数：7
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