On the Diophantine equation $f(x)f(y)=f(z)^n$ involving Laurent polynomials, II
Volume 158 / 2019
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 $n=2$.
