Let
![a, b, c, d,m, n \in \mathbb{Z}^+](/media/m/c/2/6/c26ce3e0fc41304c3f7c99f5e3eb41f6.png)
such that
![a+b+c+d = m^2,](/media/m/0/6/4/0649d53b69a4e635d3fb4299d08216b8.png)
and the largest of
![a, b, c, d](/media/m/a/b/a/aba147d136d904768670353792ec9289.png)
is
![n^2.](/media/m/9/2/1/92189009af647ac017033269a224c069.png)
Determine, with proof, the values of
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
and
%V0
Let $a, b, c, d,m, n \in \mathbb{Z}^+$ such that $$a^2+b^2+c^2+d^2 = 1989,$$
$$a+b+c+d = m^2,$$ and the largest of $a, b, c, d$ is $n^2.$ Determine, with proof, the values of $m$ and $n.$