CO-MO 2020 Problem 3

A number is said to be triangular if it can be expressed in the form $1 + 2 +...+n$ for some positive integer $n$ . We call a positive integer $a$ retriangular if there exists a fixed positive integer $b$ such that $aT +b$ is a triangular number whenever $T$ is a triangular number. Determine all retriangular numbers.