Question 28
Determine all functions $f$ from the set of non-negative integers to itself such that
$$
f(a + b) = f(a) + f(b) + f(c) + f(d),
$$
whenever $a$, $b$, $c$, $d$ are non-negative integers satisfying $2ab = c^2 + d^2$.
$$
f(a + b) = f(a) + f(b) + f(c) + f(d),
$$
whenever $a$, $b$, $c$, $d$ are non-negative integers satisfying $2ab = c^2 + d^2$.