Square Sum Is Square
It is well known that there exist pairs of distinct squares that add to make another square.
For example, $5^2 + 12^2 = 25 + 144 = 169 = 13^2$.
But this can be extended to any number of squares. For example, $2^2 + 5^2 + 14^2 = 15^2$.
Prove that there exists a sum of $n$ distinct squares that is also square.