Sums that are pythagorean and normal I noticed that
$3^2+4^2+15^2=9^2+13^2$
and also
$3+4+15=9+13$
Is there an easy way to find all pairs of disjoint sets of positive integers whose sum are the same and whose sum of squares are the same? How common are they?

set of equations:
$\left\{\begin{aligned}&x+y+z=a+b\\&x^2+y^2+z^2=a^2+b^2\end{aligned}\right.$
Solutions and can be written as follows.
$x=t+qk+qt+k$
$y=t$
$z=qk$
$a=t+qk+k$
$b=t+qk+qt$
And more:
$z=kq$
$y=(k+q+t)^2$
$x=t^2+kq+tk+qt$
$a=k^2+2qk+t^2+qt+2kt$
$b=q^2+2qk+t^2+2qt+kt$
$k,t,q$ - are integers and can be any mark.
