## Pythagorean triples – Equal products of two legs and hypotenuse?

The following integers

$a_1 \; = \; p^2 \; - \; q^2$
$b_1 \; = \; 2 \, p \, q$
$c_1 \; = \; p^2 \; + \; q^2$

$a_2 \; = \; r^2 \; - \; s^2$
$b_2 \; = \; 2 \, r \, s$
$c_2 \; = \; r^2 \; + \; s^2$

define two right triangles   $(a_1, \; b_1, \; c_1)$,   $(a_2, \; b_2, \; c_2)$

Can you find a pair of Pythagorean triples with equal products of two legs and hypotenuse:

$(p \,q) \,(p^2 - q^2)\,(p^2 + q^2) \; = \; (r \,s) \,(r^2 - s^2)\,(r^2 + s^2)$

Is it possible to find a pair of primitive Pythagorean triples?