IMO Shortlist 1983 problem 15


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2. travnja 2012.
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Decide whether there exists a set M of positive integers satisfying the following conditions:

(i) For any natural numberm >1 there are a, b \in M such that a+b = m.

(ii) If a, b, c, d \in M , a, b, c, d > 10 and a + b = c + d, then a = c or a = d.
Izvor: Međunarodna matematička olimpijada, shortlist 1983