IMO Shortlist 1992 problem 15


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2. travnja 2012.
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Does there exist a set M with the following properties?

(i) The set M consists of 1992 natural numbers.
(ii) Every element in M and the sum of any number of elements have the form m^k (m, k \in \mathbb{N}, k \geq 2).
Izvor: Međunarodna matematička olimpijada, shortlist 1992