  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 which are triangular
numbers. If the multiplier is a squared integer, there is either one or no
solution, depending on the multiplier value. Instead of recurrent relations, we
develop in this paper closed form equations to calculate directly the values of
triangular numbers and their indices without the need of knowing the previous
solutions. We develop the theoretical equations for four cases of ranks from 1
to 4 and we give several examples for non-square multipliers 2, 3, 5 and 8.

General Mathematics