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March 7th, 2010, 03:44 AM   #1
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mathematic induction

Hello,

I don't know how to continue:

Prove by mathematical induction that http://img230.imageshack.us/img230/6089/46951789.png is divisible by 6.

I thought you have to use n = n+1 but I don't know how to continue.

Does somebody know? thanks
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March 7th, 2010, 04:10 AM   #2
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Re: mathematic induction

If you show me what you have so far, I'll do my best to help.

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March 7th, 2010, 05:28 AM   #3
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Re: mathematic induction

Firstly, I did n = 1 so 5^1 + 1 = 6

Then I rewrote it to 5^2(n+1)-1 > (25)5^2n + 1 and then I kinda got stuck lol..
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March 7th, 2010, 09:07 AM   #4
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Re: mathematic induction

You're pretty much there. I refer to two things:

First, if a divides the product bc, but the gcd(a,b) = 1, what do we know about a and c?

Second, what does your inductive hypothesis state? And how do we use that? For any proof by induction, we must use our hypothesis in some form or fashion.

Is that clear enough? If not, I would recommend writing out your inductive hypothesis explicitly, and see if you can come up with something where it becomes useful. (easier than it sounds)
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March 7th, 2010, 01:29 PM   #5
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Re: mathematic induction

5^(2n+1) +1=25[5^(2n-1)] +1=25[5^(2n-1)+1] -24.
[5^(2n-1)+1] is divisible by 6 (induction hypothesis).
24 is divisible by 6.
Result is divisible by 6.
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