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 March 7th, 2010, 03:44 AM #1 Newbie   Joined: Mar 2010 Posts: 2 Thanks: 0 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
 March 7th, 2010, 04:10 AM #2 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 Re: mathematic induction If you show me what you have so far, I'll do my best to help. $6 \mid (5^{2n-1} + 1)$
 March 7th, 2010, 05:28 AM #3 Newbie   Joined: Mar 2010 Posts: 2 Thanks: 0 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..
 March 7th, 2010, 09:07 AM #4 Senior Member   Joined: Apr 2008 Posts: 435 Thanks: 0 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)
 March 7th, 2010, 01:29 PM #5 Global Moderator   Joined: May 2007 Posts: 6,806 Thanks: 716 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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