Question: prove that 8^n-1 is divisible by 7?
Answer: Prove by induction that 8n−1 is divisible by 7 Hint: It is easy to represent divisibility by 7 in the following way: 8n−1=7⋅k where k is a positive integer. ... If n=1 and k=2 for example, then we end up with 7=14 which is obviously invalid.