Question 35
Find all ordered 4-tuples of integers $(a, b, c, d)$ (not necessarily distinct) satisfying the following system of equations:
$$
\begin{aligned}
a^{2}-b^{2}-c^{2}-d^{2} & = c-b-2 \\
2 a b & = a-d-32 \\
2 a c & = 28-a-d \\
2 a d & = b+c+31
\end{aligned}
$$
$$
\begin{aligned}
a^{2}-b^{2}-c^{2}-d^{2} & = c-b-2 \\
2 a b & = a-d-32 \\
2 a c & = 28-a-d \\
2 a d & = b+c+31
\end{aligned}
$$