Question: prove that 2^3n-1 is divisible by 7?
Answer: P(k): 23k – 1 is divisible by 7. ... = 7(8m + 1), which is divisible by 7. Thus, P(k + 1) is true whenever P(k) is true. So, by the principle of mathematical induction P(n) is true for all natural numbers n.