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

• Autorzy: Maciej Ulas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11G99: None of the above, but in this section
• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 1
• Strony: 1-6

Daty

wydano

2007

Twórcy

autor

Maciej Ulas

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Identyfikatory

DOI

10.4064/cm107-1-1