For all positive non-square integer multipliers, there are infinitely many triangular numbers that are multiples of other triangular numbers. With a simple change of variables, one obtains a Pell equation, whose odd solutions provide the indices of the many infinitely triangular numbers multiple of other triangular numbers. General algebraic expressions of fundamental solutions of Pell equations are found for the multiplier expressed in function of the closest integer square. Finally, recurrent relations yielding the triangular numbers and their multiples and indices are calculated for non-square multipliers.
