Question 3
Let $a \gt b \gt c \gt d$ be positive integers that satisfy
$$
a + b + c + d = 502 \text{ and } a^2 - b^2 + c^2 - d^2 = 502.
$$
Calculate how many possible values of $a$ are.
$$
a + b + c + d = 502 \text{ and } a^2 - b^2 + c^2 - d^2 = 502.
$$
Calculate how many possible values of $a$ are.