Question 136
At the beginning we have a triple of pairwise distinct positive integers $(a, b, c)$ which satisfies $a + b + c = 2015$. Then in each step we replace the current triple of numbers $(x, y, z)$ with the triple $(y + z - x, z + x - y, x + y - z)$. At least how many steps must we make so that starting with a triple $(a, b, c)$ we will certainly get a triple which has at least one negative number?