The function \(f_{}^{}\) has the property that, for each real number \(x,\,\)

\(f(x)+f(x-1) = x^2\,\).

If \(f(19)=94,\,\) what is the remainder when \(f(94)\,\) is divided by 1000?

(第十二届AIME1994 第3题)