Question 1
(AUS 6) Let $f$ be a function that satisfies the following conditions:
(i) If $x\gt y$ and $f(y)-y\ge v\ge f(x)-x$, then $f(z)=v+z$, for some number $z$ between $x$ and $y$.
(ii) The equation $f(x)=0$ has at least one solution, and among the solutions of this equation, there is one that is not smaller than all the other solutions;
(iii) $f(0)=1$.
(iv) $f(1987)\le1988$.
(v) $f(x)f(y)=f(xf(y)+yf(x)-xy)$.
Find $f(1987)$.
(i) If $x\gt y$ and $f(y)-y\ge v\ge f(x)-x$, then $f(z)=v+z$, for some number $z$ between $x$ and $y$.
(ii) The equation $f(x)=0$ has at least one solution, and among the solutions of this equation, there is one that is not smaller than all the other solutions;
(iii) $f(0)=1$.
(iv) $f(1987)\le1988$.
(v) $f(x)f(y)=f(xf(y)+yf(x)-xy)$.
Find $f(1987)$.