Prove that there are an infinite number of distinct ordered pairs (m, n) of integers such that, for every positive integer t, the number mt + n is a triangular number if and only if t is a triangular number as well

(In reply to

What's a triangular number? by Bryan)

Triangular numbers are 1, 1+2, 1+2+3, 1+2+3+4, 1+2+3+4+5, and so on; the n-th number is ½n(n+1).