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 Solution by Old Original Oskar!)

9*3+1=28=1+2+3+4+5+6+7 so with m=9, n=1, and t=3 we have m*t+n=triangular, so it is not the case that for every positive integer t, the number  m*t+n is a triangular number if and only if t=1.

Perhaps there is an error in the problem statement and you showed what was really intended?

Edited on October 26, 2004, 7:14 pm

Posted by Richard on 2004-10-26 18:41:36