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September 19th, 2011, 08:59 AM   #1
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Proof by Induction - Divisibility Proofs

Q. Prove by induction that... (see attachment)

Notes: For the line beginning "Show that n = k + 1..." I think I may have gone wrong in the calculation here, but I'm not exactly sure.
Thank you.
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September 19th, 2011, 09:19 AM   #2
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Re: Proof by Induction - Divisibility Proofs

We need to prove by induction:

where

You have already shown the base case is valid. Thus, our induction hypothesis is:



Let's add a multiple of 8 to each side:





We have derived from completing the proof by induction.
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September 19th, 2011, 10:20 AM   #3
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Re: Proof by Induction - Divisibility Proofs

Thank you for the help. Much obliged.
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