Chapter 12.9, Problem 4CFU

To determine

To restate: the given conjecture.

Answer to Problem 4CFU

  $8^n-1=7k$

Explanation of Solution

Given information:

For all positive integers $n$ , $8^n-1$ is divisible by 7 by using the definition of divisibility.

Calculation:

For all positive integers $n$ , $8^n-1$ is divisible by 7 only if there is an integer $k$ such that $8^n-1=7k$ .

Thus, the conjecture can be restated as $8^n-1=7k$ .