Let f:Z→Z be a function satisfying f(0)=0=f(1). Assume also that f satisfies equations (A) and (B) below. \begin{eqnarray*}f(xy) = f(x) + f(y) -f(x) f(y)\qquad\mathbf{(A)}\\
f(x-y) f(x) f(y) = f(0) f(x) f(y)\qquad\mathbf{(B)}
\end{eqnarray*} for all integers x,y.(i) Determine explicitly the set {f(a) : a∈Z}.
(ii) Assuming that there is a non-zero integer a such that f(a)=0, prove that the set {b : f(b)=0} is infinite. functional equationisiISI entrance