(70 pt., 14 pt. each) Prove each of the following statements using induction. For each statement, answer the following questions.

a. (3 pt.) Complete the basis step of the proof.

b. (3 pt.) What is the inductive hypothesis?

c. (3 pt.) What do you need to show in the inductive step of the proof?

d. (5 pt.) Complete the inductive step of the proof.

1. Prove that = + = for any nonnegative integer . (please answer it in parts a,b,c, and d )

2. 4. Prove that + is divisible by for any positive integer . Recall that an integer is divisible by an integer with if and only if there exists an integer such that = . (please answer it in parts a,b,c and d)