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) (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 
.
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