I'm asked to generate Pythagorean triples from the polynomial identity:
$$(X^2-1)^2 + (2X)^2=(X^2+1)^2$$ By substituting rational numbers $\frac p q$ for $X$. However, Pythagorean triples are just as the name says, it, three numbers. If I would substitute this number I get: $$(\left(\frac p q\right)^2-1)^2 + 4\left(\frac p q\right)^2=(\left(\frac p q\right)^2+1)^2$$
How would I get three integers from this? There are just two numbers involved, $p$ and $q$.