May 16th, 2017, 06:41 PM  #1 
Newbie Joined: May 2017 From: Trinidad Posts: 1 Thanks: 0  Induction
Prove that, for all positive integers n,3^2n  1 is divisible by 8

May 16th, 2017, 07:08 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,709 Thanks: 458  Easier by modular arithmetic. $3^{2n} = (3^2)^n \equiv 1^n \equiv 1 \pmod 8$. Did you make any progress on your induction?
Last edited by Maschke; May 16th, 2017 at 07:13 PM. 
May 17th, 2017, 03:10 AM  #3  
Senior Member Joined: May 2016 From: USA Posts: 904 Thanks: 359  Quote:
$3^2 * 2  1 = 9 * 2  1 = 17.$ Not divisible by 8. $ 3^2 * 3  1 = 9 * 3  1 = 26.$ Not divisible by 8. There are two overall steps in a proof by induction. What is the first one? What did you get in that step? What is the second step? The second step is always where the difficulty lies. How do you initiate that step? Last edited by JeffM1; May 17th, 2017 at 03:14 AM.  

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