Give an example of a statement P(n) which is true for all n. Justify your answer. Prove each of the statements in Exercises 3 to 16 by the Principle of Mathematical Induction:

Give an example of a statement P(n) which it true for all n ≥ 4 but P(1), P(2) and P(3) are not true. Justify your answer.

4ⁿ – 1 is divisible by 3, for each natural number n.

2³ⁿ – 1 is divisible by7, for all natural numbers n.

n³ – 7n + 3 is divisible by 3, for all natural numbers n.