MathDB

84

Part of 1990 IMO Longlists

Problems(1)

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

Source:

9/19/2010
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.
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