MathDB

15

Part of 1992 IMO Shortlist

Problems(1)

Every element in M, sum of any number with form m^k

Source: IMO Shortlist 1992, Problem 15

8/13/2008
Does there exist a set M M with the following properties? (i) The set M M consists of 1992 natural numbers. (ii) Every element in M M and the sum of any number of elements have the form mk m^k (m,k∈N,k≥2). (m, k \in \mathbb{N}, k \geq 2).
number theoryPerfect PowersAdditive combinatoricsAdditive Number TheoryIMO ShortlistIMO Longlist