IMO Shortlist 1987 problem 18


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2. travnja 2012.
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For any integer r \geq 1, determine the smallest integer h(r) \geq 1 such that for any partition of the set \{1, 2, \cdots, h(r)\} into r classes, there are integers a \geq  0 \ ; 1 \leq x \leq y, such that a + x, a + y, a + x + y belong to the same class.

Proposed by Romania
Izvor: Međunarodna matematička olimpijada, shortlist 1987