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Periodica Mathematica Hungarica

, Volume 75, Issue 2, pp 295–301 | Cite as

On the Diophantine system \(f(z)\,{=}\,f(x)f(y)\,{=}\,f(u) f(v)\)

  • Yong ZhangEmail author
  • Zhongyan Shen
Article
  • 108 Downloads

Abstract

We show that the Diophantine system
$$\begin{aligned} f(z)=f(x)f(y)=f(u)f(v) \end{aligned}$$
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.

Keywords

Diophantine system Positive integer solution Rational solution Elliptic curve 

Mathematics Subject Classification

Primary 11D25 Secondary 11D72 11G05 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsChangsha University of Science and TechnologyChangshaPeople’s Republic of China
  2. 2.Department of MathematicsZhejiang International Studies UniversityHangzhouPeople’s Republic of China

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