Question 46
(ROM 5) If $x,y,z$ are real numbers satisfying the relations $x+y+z=1$ and $\arctan x+\arctan y+\arctan z=\pi/4$, prove that
$$x^{2n+1}+y^{2n+1}+z^{2n+1}=1$$
for all positive integers $n$.
$$x^{2n+1}+y^{2n+1}+z^{2n+1}=1$$
for all positive integers $n$.