MathDB
IMC 2011 Day 1 Problem 5

Source:

July 30, 2011
vectoralgebrapolynomialfunctionabstract algebraanalytic geometryinduction

Problem Statement

Let nn be a positive integer and let VV be a (2n−1)(2n-1)-dimensional vector space over the two-element field. Prove that for arbitrary vectors v1,…,v4n−1∈V,v_1,\dots,v_{4n-1} \in V, there exists a sequence 1≤i1<⋯<i2n≤4n−11\leq i_1<\dots<i_{2n}\leq 4n-1 of indices such that vi1+⋯+vi2n=0.v_{i_1}+\dots+v_{i_{2n}}=0.
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