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

Volume 158 / 2019

Yong Zhang, Arman Shamsi Zargar Colloquium Mathematicum 158 (2019), 119-126 MSC: Primary 11D72, 11D25; Secondary 11D41, 11G05. DOI: 10.4064/cm7528-10-2018 Published online: 23 July 2019

Abstract

We investigate the non-trivial rational parametric solutions of the Diophantine equation $f(x)f(y)=f(z)^n$, where $f=x^k+ax^{k-1}+b/x$, $k\geq 2$, $x^2+a/x+b/x^2$ for $n=1$, and $f=x^2+ax+b+a^3/(27x)$, $x^2+ax+b+a^3/(16x)+a^4/(256x^2)$ for $n=2$.

Authors

  • Yong ZhangSchool of Mathematics and Statistics
    Changsha University of Science and Technology
    Hunan Provincial Key Laboratory
    of Mathematical Modeling
    and Analysis in Engineering
    Changsha 410114, People’s Republic of China
    e-mail
  • Arman Shamsi ZargarDepartment of Mathematics
    and Applications
    Faculty of Science
    University of Mohaghegh Ardabili
    Ardabil 56199-11367, Iran
    e-mail

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