MEMO 2008 ekipno problem 6


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28. travnja 2012.
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On a blackboard there are n \geq 2, n \in \mathbb{Z}^{+} numbers. In each step we select two numbers from the blackboard and replace both of them by their sum. Determine all numbers n for which it is possible to yield n identical number after a finite number of steps.
Izvor: Srednjoeuropska matematička olimpijada 2008, ekipno natjecanje, problem 6