Suppose that we color integers 1, 2, 3, …, n with three colors so that each color is given to **more than** n/4 integers. Prove that there exist x, y, z such that x+y=z and x,y,z have distinct colors.

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Suppose that we color integers 1, 2, 3, …, n with three colors so that each color is given to **more than** n/4 integers. Prove that there exist x, y, z such that x+y=z and x,y,z have distinct colors.

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