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## 'Triangular Triples' printed from http://nrich.maths.org/

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.]