3. The function $f$ has the following property: 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?
3. From the given, $f(x+1)=(x+1)^{2}-f(x), f(x+2)=(x+2)^{2}-f(x+1)=$ $(x+2)^{2}-(x+1)^{2}+f(x) \cdots$, generally, we have $f(x+m)=(x+m)^{2}-(x+m-1)^{2}$ $+\cdots+(-1)^{m-1}(x+1)^{2}+(-1)^{m} f(x)$. Therefore, $f(94)=f(19+75)=4561$, from which we can conclude that the remainder of $f(94)$ divided by 1000 is 561.