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August 12th, 2011, 11:00 AM   #1
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How to proof this is true by induction **STUCK**

Hi guys, first of all thanks for your help. I'm stuck with this problem, i need to proof the following:

5^(n+1) + 2 * 3^n + 1 is divisible by 8 for any n >= 0

It's true for n = 0
5 + 2 + 1 = 8

How to proof that it's true for n+1 ??

Thanks!!
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August 12th, 2011, 11:20 AM   #2
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Re: How to proof this is true by induction **STUCK**

I would set my induction hypothesis as:

where

Then compute:



Now, we may write:

where since the sum of two odd numbers is even, thus adding equivalent expressions to both sides of the induction hypothesis, we have:





Since we have derived from this completes the proof by induction.
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August 12th, 2011, 11:52 AM   #3
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Re: How to proof this is true by induction **STUCK**

Thanks Mark!
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August 12th, 2011, 11:57 AM   #4
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Re: How to proof this is true by induction **STUCK**

Glad to help, and welcome to the forum!
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