Question 84
Prove that there exists exactly one polynomial $P(x)$ with real coefficients for which the polynomial
$$
(x+y)^{1000}-P(x)-P(y)
$$
is divisible by the polynomial $x y-x-y$.
$$
(x+y)^{1000}-P(x)-P(y)
$$
is divisible by the polynomial $x y-x-y$.