Question 12
Let $a,b,c,d$ be positive integers such that $a>b>c>d$ which satisfy the following system of equations: $$\begin{cases}a+b+c+d=2020\\a^2-b^2+c^2-d^2=2020.\end{cases}$$ How many ordered quadruples $(a,b,c,d)$ are there that satisfy the conditions?