Problem 3

It is possible to write $15129 = 123^2$ as the sum of three distinct squares: $15129 = 27^2 + 72^2 + 96^2$.

(i) By using the identity $(a + b)^2 = a^2 + 2ab + b^2$, or otherwise, find another way to write $15129$ as the sum of three distinct squares.

(ii) Hence, or otherwise, show that $378225 = 615^2$ can be written as the sum of six distinct squares.