IMO 1985 LL ROM71

For every integer r > 1 find the smallest integer h(r) > 1

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IMO 1985 LL ROM71

Origin: ROM

Problem

For every integer r > 1 find the smallest integer h(r) > 1 having the following property: For any partition of the set {1, 2, . . ., h(r)} into r classes, there exist integers a \geq0, 1 \leqx \leqy such that the numbers a + x, a + y, a + x + y are contained in the same class of the partition.