Question 121
Let the function $f: \mathbb{Z} \rightarrow \mathbb{Z}$ take only integer inputs and have integer outputs. For any integers $x$ and $y$, $f$ satisfies
$$
f(x)+f(y)=f(x+1)+f(y-1)
$$
If $f(2016)=6102$ and $f(6102)=2016$, what is $f(1)$?
$$
f(x)+f(y)=f(x+1)+f(y-1)
$$
If $f(2016)=6102$ and $f(6102)=2016$, what is $f(1)$?