Question 90
Show that there are infinitely many positive integers $c$, such that both of the following equations have solutions in positive integers:
$$
\left(x^{2}-c\right)\left(y^{2}-c\right)=z^{2}-c
$$
and
$$
\left(x^{2}+c\right)\left(y^{2}-c\right)=z^{2}-c.
$$
$$
\left(x^{2}-c\right)\left(y^{2}-c\right)=z^{2}-c
$$
and
$$
\left(x^{2}+c\right)\left(y^{2}-c\right)=z^{2}-c.
$$