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.
"Three triangular numbers contained in geometric progression." Funct. Approx. Comment. Math. 42 (1) 59 - 65, March 2010. https://doi.org/10.7169/facm/1269437069