Question 19
Each vertex of a pentagon is assigned an integer, so that the sum of the five integers is positive. If three consecutive vertices have assigned numbers $x, y, z$, respectively, and is $y\lt 0$, then the following operation is allowed to do: The numbers $x, y, z$ are replaced respectively by $x+y$, $-y$, $z+y$. This operation can be done repeatedly while at least one of the five numbers is negative. Determine if this process necessarily ends a finite number of steps.