Question 57
Given positive integers $a$, $b$, $c$ which are pairwise coprime. Let $f(n)$ represent the number of nonnegative integer solutions $(x, y, z)$ of the equation $a x + b y + c z = n$. Prove: there exist real constants $\alpha$, $\beta$, $\gamma$, such that for every nonnegative real number $n$,
$$
|f(n) - (\alpha n^2 + \beta n + \gamma)| \lt \frac{a+b+c}{12}.
$$
$$
|f(n) - (\alpha n^2 + \beta n + \gamma)| \lt \frac{a+b+c}{12}.
$$