MathDB

Each integer is colored with exactly one of

3

possible colors -- black, red or white -- satisfying the following two rules : the negative of a black number must be colored white, and the sum of two white numbers (not necessarily distinct) must be colored black.
(a) Show that, the negative of a white number must be colored black and the sum of two black numbers must be colored white.
(b) Determine all possible colorings of the integers that satisfy these rules.

Problem Statement