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. combinatoricsIntegersnumber theoryIndonesiaIndonesia MOInamo