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A Conjectured of Sierpinski on Triangular Numbers(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2007年02期
Page:
33-36
Research Field:
数学
Publishing date:

Info

Title:
A Conjectured of Sierpinski on Triangular Numbers
Author(s):
Yang Shichun; He Bo
Department of Mathematics,ABa Teacher’s College,Sichuan Wenchuan 623000,China
Keywords:
triangular number;  geometric p rogression;  Sierp inski question;  Pell equation;  p rivitive divi sor
PACS:
O156
DOI:
-
Abstract:
The study of triangular number p romblem is very activing. Recently, Bennett p roved a conjec ture of Sierp inski on triangular numbers. In this paper, we firstly modified the mistake in reference of Bennett, then using Strömer’s theorem of the solutions of Pell equation, and a deep result of p rivitive divi sor of Bilu, Hanrot and Voutier, we p roved that there is no exist four distinct triangular numbers in geo metric p rogression, therefore we sovled the question of Sierp inski on triangular numbers

References:

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Last Update: 2013-05-05