



 
Hi Luke, Note that triangular numbers are of the form $\frac{n(n1)}{2}$ (so actually depending on the parity of $n, \frac{n}{2} \times (n1)$ or $n \times \frac{(n1)}{2}).$ The second thing to note is that $n$ and $n1$ are relatively prime, i.e., they have no common divisors beyond 1. So if a number is a perfect square and a triangular number what does that say about each of the factors $\frac{n}{2}$ and $(n1)$ (or $n$ and $\frac{n1}{2}$)? Once you see this you will narrow your search down and find the next one quickly. Penny  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 