Question 131
For how many quadruples $(a, b, c, d)$ of non-negative integers are the three expressions $a^{2}-c^{2}$, $b^{2}-d^{2}$ and $a b+b c+c d+d a$ all equal to $1024$?
(A) $0$
(B) $1$
(C) $4$
(D) $9$
(E) $11$
(A) $0$
(B) $1$
(C) $4$
(D) $9$
(E) $11$