MathDB
ASU 063 All Russian MO 1965 x_{i,j}+x_{j,k}+x_{k,i}=0

Source:

June 19, 2019
algebrasystem of equations

Problem Statement

Given n2n^2 numbers xi,jx_{i,j} (i,j=1,2,...,ni,j=1,2,...,n) satisfying the system of n3n^3 equations xi,j+xj,k+xk,i=0   (i,j,k=1,...,n)x_{i,j}+x_{j,k}+x_{k,i}=0 \,\,\, (i,j,k = 1,...,n)Prove that there exist such numbers a1,a2,...,ana_1,a_2,...,a_n, that xi,j=ai−ajx_{i,j}=a_i-a_j for all i,j=1,...ni,j=1,...n.
Back to ProblemsView on AoPS