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

Source: IMO Shortlist 1992, Problem 15

August 13, 2008
number theoryPerfect PowersAdditive combinatoricsAdditive Number TheoryIMO ShortlistIMO Longlist

Problem Statement

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).
Back to ProblemsView on AoPS