MathDB

Each integer is colored with exactly one of the following colors: red, blue, or orange, and all three colors are used in the coloring. The coloring also satisfies the following properties:
1. The sum of a red number and an orange number results in a blue-colored number, 2. The sum of an orange and blue number results in an orange-colored number; 3. The sum of a blue number and a red number results in a red-colored number.
(a) Prove that

0

and

1

must have distinct colors. (b) Determine all possible colorings of the integers which also satisfy the properties stated above.

Problem Statement