MathDB
Exist numbers their sum is divisible by 2n - ILL 1990 SWE2

Source:

September 19, 2010
number theory proposednumber theory

Problem Statement

Let n≥4n \geq 4 be an integer. a1,a2,…,an∈(0,2n)a_1, a_2, \ldots, a_n \in (0, 2n) are nn distinct integers. Prove that there exists a subset of the set {a1,a2,…,an}\{a_1, a_2, \ldots, a_n \} such that the sum of its elements is divisible by 2n.2n.
Back to ProblemsView on AoPS