Question 103
Let $m, n$ be positive integers and $x, y, z \in [0, 1]$ be real numbers. Prove that
$$
0 \le x^{m+n} + y^{m+n} + z^{m+n} - x^m y^n - y^m z^n - z^m x^n \le 1
$$
and find when equality holds.
$$
0 \le x^{m+n} + y^{m+n} + z^{m+n} - x^m y^n - y^m z^n - z^m x^n \le 1
$$
and find when equality holds.