A note on Sierpiński problem related to triangular numbers

Simple item page
dc.creatorUlas, Maciej
dc.date2008-10-01
dc.date.accessioned2026-07-07T10:06:44Z
dc.date.available2026-07-07T10:06:44Z
dc.descriptionIn this note we show that the system of equations t_{x}+t_{y}=t_{p},\quad t_{y}+t_{z}=t_{q},\quad 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 rational three-parametric solution. Using this result we show that the system t_{x}+t_{y}=t_{p},\quad t_{y}+t_{z}=t_{q},\quad t_{x}+t_{z}=t_{r},\quad t_{x}+t_{y}+t_{z}=t_{s} has infinitely many rational two-parametric solutions.
dc.descriptionsubmitted
dc.identifierhttps://arxiv.org/abs/0810.0222
dc.identifierhttp://arxiv.org/abs/0810.0222
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170424
dc.subjectNumber Theory
dc.subject11D41;11D72
dc.titleA note on Sierpiński problem related to triangular numbers
dc.typetext

Files

Collections

arXiv