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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


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.


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

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