True or False

Let P(n) be a statement and let P(k) ⟹ P(k + 1), for some natural number k, then P(n) is true of all n ϵ N.

If 10ⁿ + 3.4ⁿ⁺² + k is divisible by 9 for all n ϵ N, then the least positive integral value of k is

For all n ϵ N, 3.5^{2n + 1} + 23^{n + 1} is divisible by

If xⁿ – 1 is divisible by x – k, then the least positive integral value of k is

Fill in the blanks in the following:

If P(n) : 2n < n!, n ϵ N, then P(n) is true for all n ≥ __________.