MathDB
real number with a partition condition

Source: IMS 2007

May 18, 2007
searchnumber theorylinear algebralinear algebra unsolved

Problem Statement

x1,x2,…,xnx_{1},x_{2},\dots,x_{n} are real number such that for each ii, the set {x1,x2,…,xn}\{xi}\{x_{1},x_{2},\dots,x_{n}\}\backslash \{x_{i}\} could be partitioned into two sets that sum of elements of first set is equal to the sum of the elements of the other. Prove that all of xix_{i}'s are zero. [hide="Hint"]It is a number theory problem.
Back to ProblemsView on AoPS