Question 70
Find all quadruples of integers $a, b, c$ and $d$ that solve the system of equations
$$
\begin{aligned}
& a^{2}+b^{2}+c^{2}=d+13 \\
& a+2 b+3 c=\frac{d}{2}+13
\end{aligned}
$$
$$
\begin{aligned}
& a^{2}+b^{2}+c^{2}=d+13 \\
& a+2 b+3 c=\frac{d}{2}+13
\end{aligned}
$$