Determine the smallest positive integer $n$ such that, for any coloring of the elements of the set $\{2,3,...,n\}$ with two colors, the equation $x + y = z$ has a monochrome solution with $x \ne y$. (We say that the equation $x + y = z$ has a monochrome solution if there exist $a, b, c$ distinct, having the same color, such that $a + b = c$.)