Prove that the set of positive integers cannot be partitioned into three nonempty subsets such that, for any two integers
taken from two different subsets, the number
belongs to the third subset.
%V0
Prove that the set of positive integers cannot be partitioned into three nonempty subsets such that, for any two integers $x,y$ taken from two different subsets, the number $x^2-xy+y^2$ belongs to the third subset.
Školjka