SOLUTION: Use mathematical induction to prove each of the following: Fore each natural number n, 3 divides (4^(n)-1)

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Question 1053445: Use mathematical induction to prove each of the following:
Fore each natural number n, 3 divides (4^(n)-1)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Base case n = 1:
3 divides , which is correct.

Inductive step: n = k+1:
Suppose 3 divides for some . Then for some integer m. Multiply by 4 and we have that . Add 3 to both sides to get . Since the right-hand side is a multiple of 3, so is the left-hand side. Therefore 3 divides .