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On the Diophantine equation $f(x)f(y)=f(z)^n$ involving Laurent polynomials

Volume 151 / 2018

Yong Zhang Colloquium Mathematicum 151 (2018), 111-122 MSC: Primary 11D72, 11D25; Secondary 11D41, 11G05. DOI: 10.4064/cm6920-1-2017 Published online: 24 November 2017

Abstract

Using the theory of elliptic curves, we investigate nontrivial rational parametric solutions of the Diophantine equation $f(x)f(y)=f(z)^n$, where $n=1,2$ and $f(X)$ are some simple Laurent polynomials.

Authors

  • Yong ZhangCollege of Mathematics and Computing Science
    Changsha University of Science and Technology
    410114 Changsha, People’s Republic of China
    and
    Department of Mathematics
    Zhejiang University
    310027 Hangzhou, People’s Republic of China
    e-mail

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