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

• Autorzy: Yong Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11D41: Higher degree equations; Fermat's equation
• 11D72: Equations in many variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 2
• Strony: 275-283

Daty

wydano

2016

Twórcy

autor

Yong Zhang

• College of Mathematics and Computing Science, Changsha University of Science and Technology, 410114 Changsha, People's Republic of China
• Department of Mathematics, Zhejiang University, 310027 Hangzhou, People's Republic of China

Identyfikatory

DOI

10.4064/cm142-2-8