Find 7-tuples of pairwise distinct positive integers such that the sum of squares of first 4 equals sum of squares of last 3 As already stated in title, find 7-tuples ($a_1,a_2,a_3,a_4,b_1,b_2,b_3$) of pairwise distinct positive integers such that
$$a_1^2+a_2^2+a_3^2+a_4^2=b_1^2+b_2^2+b_3^2$$
This came in RMO 2016 Delhi paper where one was asked to prove that infinite such tuples exist. I have no idea how to do so.

For Diophantine equation.
$$a^2+b^2+c^2+d^2=x^2+y^2+z^2$$
You can record a parameterization.
$$a=2(p+s+r-t-q)k$$
$$b=k^2+t^2+q^2-p^2-s^2-r^2$$
$$c=p^2+s^2+r^2+t^2-k^2-q^2-2(p+s+r-q)t$$
$$d=p^2+s^2+r^2+q^2-k^2-t^2-2(p+s+r-t)q$$
$$x=p^2+k^2+t^2+q^2-s^2-r^2+2(s+r-t-q)p$$
$$y=s^2+k^2+t^2+q^2-p^2-r^2+2(p+r-t-q)s$$
$$z=r^2+k^2+t^2+q^2-p^2-s^2+2(p+s-t-q)r$$
