x1,x2,…,xn are real number such that for each i, the set {x1,x2,…,xn}\{xi} 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 xi's are zero.
[hide="Hint"]It is a number theory problem. searchnumber theorylinear algebralinear algebra unsolved