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 April 8th, 2014, 04:11 AM #1 Senior Member   Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18 Induction again Prove that (4^n) - 1 is divisible by 3 My attempt: 1) let n = 1 (4^1) - 1 = 4 - 1 = 3 3 is divisible by 3. So true for n = 1 2) Assume it is true for n = k So (4^k) - 1 is divisible by 3 3) let n = k + 1 but and are divisible by 3 so is divisible by 3 Therefore for all n 4^n - 1 is divisible by 3 Is this proof acceptable? The third step doesn't look like induction..thanks April 8th, 2014, 04:19 AM   #2
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Quote:
 Originally Posted by shunya 3) let n = k + 1 but and are divisible by 3
$4^k+1$ should be replaces by $4^k-1$ (two times). Otherwise, the proof is correct. For clarity, it would be nice to say that $3\mid(4^k-1)$ by induction hypothesis. Tags induction Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post shunya Algebra 2 April 8th, 2014 04:27 AM cool012 Algebra 0 December 1st, 2013 06:37 AM tejolson Linear Algebra 2 February 20th, 2013 11:38 AM OriaG Algebra 11 October 27th, 2012 04:55 PM gaussrelatz Algebra 4 September 28th, 2011 09:55 PM

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