MathDB
A set with at least two elements

Source: Romanian NMO 2006, Grade 7, Problem 4

April 18, 2006
calculusintegrationnumber theorygreatest common divisorleast common multiplerelatively prime

Problem Statement

Let AA be a set of positive integers with at least 2 elements. It is given that for any numbers a>ba>b, a,b∈Aa,b \in A we have [a,b]a−b∈A\frac{ [a,b] }{ a- b } \in A, where by [a,b][a,b] we have denoted the least common multiple of aa and bb. Prove that the set AA has exactly two elements. Marius Gherghu, Slatina
Back to ProblemsView on AoPS