Some observations on the Diophantine equation f(x)f(y) = f(z)²

Yong Zhang. "Some observations on the Diophantine equation f(x)f(y) = f(z)²." Colloquium Mathematicae 142.2 (2016): 275-283. <http://eudml.org/doc/283797>.

@article{YongZhang2016,
abstract = {Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + 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.},
author = {Yong Zhang},
journal = {Colloquium Mathematicae},
language = {eng},
number = {2},
pages = {275-283},
title = {Some observations on the Diophantine equation f(x)f(y) = f(z)²},
url = {http://eudml.org/doc/283797},
volume = {142},
year = {2016},
}

TY - JOUR
AU - Yong Zhang
TI - Some observations on the Diophantine equation f(x)f(y) = f(z)²
JO - Colloquium Mathematicae
PY - 2016
VL - 142
IS - 2
SP - 275
EP - 283
AB - Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + 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.
LA - eng
UR - http://eudml.org/doc/283797
ER -