# Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations

@inproceedings{Pletser2021TriangularNM, title={Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations}, author={Vladimir Pletser}, year={2021} }

For all positive non-square integer multiplier k, there is an infinity of multiples of triangular numbers which are also triangular numbers. With a simple change of variables, these triangular numbers can be found using solutions of Pell equations. With some conditions on parities of fundamental solutions of the simple and generalized Pell equations, only odd solutions of the generalized Pell equation are retained to provide many infinitely solutions found on branches corresponding to each of…

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