Each integer is colored with exactly one of three 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.