Question 850395: Use induction to show that 5^n-1 is divisible by 4.
Answer by FrankM(1040)   (Show Source):
You can put this solution on YOUR website! If you treat 5^n as (4+1)^n and use binomial expansion, you see that 4 is a factor of every term except the last term, the constant 1.
Let's look at
(4+1)^2 = 4^2+(2)(4)+1 - you see this equal 16+8+1 ?
(4+1)^3 = 4^3+(3)(4^2)+(3)(4)+1 = 64+48+12+1
So, the -1 gets the result back to being divisible by 4.
I hope that helps.
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