# Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers

@inproceedings{Pletser2020RecurrentRF, title={Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers}, author={Vladimir Pletser}, year={2020} }

We search for triangular numbers that are multiples of other triangular numbers. It is found that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers that are triangular numbers and recurrent relations are deduced theoretically. If the multiplier is a squared integer, there is either one or no solution, depending on the multiplier value.

## 3 Citations

### Closed Form Equations for Triangular Numbers Multiple of Other Triangular Numbers

- Mathematics
- 2021

Abstract. Triangular numbers that are multiple of other triangular numbers are investigated. It is known that for any positive non-square integer multiplier, there is an infinity of multiples of…

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

- Mathematics
- 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…

### Congruence properties of indices of triangular numbers multiple of other triangular numbers

- MathematicsOpen Journal of Mathematical Sciences
- 2021

For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple of other triangular numbers. We analyze the congruence properties of indices \(\xi\) of triangular…

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