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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. 
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: 6,709 Thanks: 675  Re: mathematic induction
5^(2n+1) +1=25[5^(2n1)] +1=25[5^(2n1)+1] 24. [5^(2n1)+1] is divisible by 6 (induction hypothesis). 24 is divisible by 6. Result is divisible by 6. 

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