Geodesic
Some observations on the Diophantine equation $f(x)f(y)=f(z)^2$
Yong Zhang1
1College 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
Colloquium Mathematicum, Tome 142 (2016) no. 2, pp. 275-283

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

DOI

Let $f\in \mathbb {Q}[X]$ be a polynomial without multiple roots and with $\mathop{\rm deg}(f)\geq 2$. We give conditions for $f(X)=AX^2+BX+C$ such that the Diophantine equation $f(x)f(y)=f(z)^2$ has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider $f(x)f(y)=f(z)^2$ for quartic polynomials.
DOI : 10.4064/cm142-2-8
Keywords: mathbb polynomial without multiple roots mathop deg geq conditions diophantine equation y has infinitely many nontrivial integer solutions prove equation has rational parametric solution infinitely many irreducible cubic polynomials moreover consider y quartic polynomials

Yong Zhang  1

1 College 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 
Yong Zhang. Some observations on the Diophantine equation $f(x)f(y)=f(z)^2$. Colloquium Mathematicum, Tome 142 (2016) no. 2, pp. 275-283. doi: 10.4064/cm142-2-8
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