Discrete Mathematical Structures... HELP!?

Question

1) Let n be an interger. Prove that the gcd(n, n+2) =1 or gcd(n, n+2) =2

2) A chemist has five assistants engaged in the research of nine compounds that must be synthesized. In how many ways can the chemist assign the syntheses to the five assistants so that each assistant is working on at least one synthesis.

Answer 1

1) Suppose the gcd is d. Since d divides both n and n + 2, d must divide their difference, so d divides 2. Therefore, d = 1 or d = 2.