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## Homework Statement

Use mathematical induction to prove that (8n − 7n − 1) is divisible by 49 for any n ∈ N.

Correction by mentor for better readability: ##49\,|\,(8^n-7n-1)##

## The Attempt at a Solution

We can see that the base case is satisfied here:

n = 1,

8^1-7*1-1 = 0 and 49 | 0 is true since 49 | 0 => 49*a = 0 where a is an integer, here a = 0.

therefore base case is proven

Inductive assumption is : Assume true : 49 | (8

^{k}-7k - 1) for n=k

Now have to show that 49 | (8

^{k+1}- 7k - 8)

So we can see that 8

^{k+1}- 7k - 8 = 8*8

^{k}-7k -1, but I am unsure of where to go from here.

Any help will be appreciated.

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