(a) What is the maximum number of integers that can be included in a set such that no 3 of them sum to a multiple of 3? Carefully justify your answer.

(For instance, the set {2, 4, 5, 8} doesn't work because 2+5+8 is divisible by 3)

(b) What is the maximum number of integers that can be included in a set such that no 6 of them sum to a multiple of 6?