Let n≥5 be an integer and let x1,x2,...,xn be n distinct integer numbers such that no 3 of them can be in arithmetic progression. Prove that if for all 1≤i,j≤n we have 2∣xi−xj∣≤n(n−1) then there exist 4 distinct indices i,j,k,l∈{1,2,...,n} such that xi+xj=xk+xl.