On the diophantine equation f(x)f(y) = f(z)²

Maciej Ulas. "On the diophantine equation f(x)f(y) = f(z)²." Colloquium Mathematicae 107.1 (2007): 1-6. <http://eudml.org/doc/284068>.

@article{MaciejUlas2007,
abstract = {Let f ∈ ℚ [X] and deg f ≤ 3. We prove that if deg f = 2, then the diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in ℚ (t). In the case when deg f = 3 and f(X) = X(X²+aX+b) we show that for all but finitely many a,b ∈ ℤ satisfying ab ≠ 0 and additionally, if p|a, then p²∤b, the equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in rationals.},
author = {Maciej Ulas},
journal = {Colloquium Mathematicae},
keywords = {Diophantine equations; elliptic curves; geometric progression},
language = {eng},
number = {1},
pages = {1-6},
title = {On the diophantine equation f(x)f(y) = f(z)²},
url = {http://eudml.org/doc/284068},
volume = {107},
year = {2007},
}

TY - JOUR
AU - Maciej Ulas
TI - On the diophantine equation f(x)f(y) = f(z)²
JO - Colloquium Mathematicae
PY - 2007
VL - 107
IS - 1
SP - 1
EP - 6
AB - Let f ∈ ℚ [X] and deg f ≤ 3. We prove that if deg f = 2, then the diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in ℚ (t). In the case when deg f = 3 and f(X) = X(X²+aX+b) we show that for all but finitely many a,b ∈ ℤ satisfying ab ≠ 0 and additionally, if p|a, then p²∤b, the equation f(x)f(y) = f(z)² has infinitely many nontrivial solutions in rationals.
LA - eng
KW - Diophantine equations; elliptic curves; geometric progression
UR - http://eudml.org/doc/284068
ER -