A note on Sierpiński's problem related to triangular numbers

• Autorzy: Maciej Ulas
• Języki publikacji: EN

Abstrakty

EN

We show that the system of equations
$t_{x} + t_{y} = t_{p}, t_{y} + t_{z} = t_{q}, t_{x} + t_{z} = t_{r}$,
where $t_{x} = x(x+1)/2$ is a triangular number, has infinitely many solutions in integers. Moreover, we show that this system has a rational three-parameter solution. Using this result we show that the system
$t_{x} + t_{y} = t_{p}, t_{y} + t_{z} = t_{q}, t_{x} + t_{z} = t_{r}, t_{x} + t_{y}+t_{z} = t_{s}$
has infinitely many rational two-parameter solutions.

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: 2009
• Tom: 117
• Numer: 2
• Strony: 165-173

Daty

wydano

2009

Twórcy

autor

Maciej Ulas

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 67, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/cm117-2-2