Challenge Level

Three numbers a, b and c are a Pythagorean triple if $a^2+ b^2= c^2$. The triangular numbers are:

$\frac{1\times 2}{2}, \frac{2\times 3}{2}, \frac{3\times 4}{2}, \frac{4\times 5}{2}$

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

[In fact, these are the ONLY known set of three triangular numbers that form a Pythagorean triple.]