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 Brandon3 March 7th, 2010 03:44 AM

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

 jason.spade March 7th, 2010 04:10 AM

Re: mathematic induction

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

$6 \mid (5^{2n-1} + 1)$

 Brandon3 March 7th, 2010 05:28 AM

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..

 jason.spade March 7th, 2010 09:07 AM

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)

 mathman March 7th, 2010 01:29 PM

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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