Open Access
March 2010 Three triangular numbers contained in geometric progression
Jiagui Luo, Pingzhi Yuan
Funct. Approx. Comment. Math. 42(1): 59-65 (March 2010). DOI: 10.7169/facm/1269437069


In the present paper we prove that all three distinct triangular numbers in geometric progression and the positive integer solutions $(x,y,z)$ of the equation $(x^2-1)(y^2-1)= (z^2-1)^2$, $1<x<z<y$, $2\not|xyz$ are one-to-one under the assumption that a conjecture on a system of diophantine equations holds.


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Jiagui Luo. Pingzhi Yuan. "Three triangular numbers contained in geometric progression." Funct. Approx. Comment. Math. 42 (1) 59 - 65, March 2010.


Published: March 2010
First available in Project Euclid: 24 March 2010

zbMATH: 1206.11037
MathSciNet: MR2640770
Digital Object Identifier: 10.7169/facm/1269437069

Primary: 11D25
Secondary: 11D41

Keywords: geometric progressions , Pell equations , Triangular numbers

Rights: Copyright © 2010 Adam Mickiewicz University

Vol.42 • No. 1 • March 2010
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