MathDB

Let f be a function that satisfies the following conditions:

(i)

x > y

and

f(y) - y \geq v \geq 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) \leq 1988

(v)

f(x)f(y) = f(xf(y) + yf(x) - xy)

.
Find

f(1987)

.
Proposed by Australia.

1