IMO Shortlist 1992 problem 15
Dodao/la:
arhiva2. travnja 2012. Does there exist a set
with the following properties?
(i) The set
consists of 1992 natural numbers.
(ii) Every element in
and the sum of any number of elements have the form
%V0
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
Školjka 
