My Math Forum Impossible proof by induction

 Algebra Pre-Algebra and Basic Algebra Math Forum

 October 3rd, 2015, 02:46 PM #1 Newbie   Joined: Oct 2015 From: milton keynes Posts: 2 Thanks: 0 Impossible proof by induction Prove (3^k ) + (7 ^ (k-1)) + 8 is divisible by 12. Last edited by skipjack; October 3rd, 2015 at 03:08 PM.
 October 3rd, 2015, 02:50 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra Why is this impossible?
 October 3rd, 2015, 04:26 PM #3 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 True for k=1. Assume true for k, show true for k+1 (for k+1) $\displaystyle 3(3^k)+7(7^{k-1})+8$ divisible by 12? Subtract assumption for k and get $\displaystyle 2(3^k)+6(7^{k-1})$ divisible by 12? Expression is $\displaystyle 6(3^{k-1}+7^{k-1})$ Term inside parentheses is even! Therefore 6x term is divisible by 12!

 Tags impossible, induction, proof

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Tiome_nguyen Abstract Algebra 3 June 2nd, 2012 09:14 AM Spaghett Number Theory 1 October 19th, 2011 07:19 PM Airmax Applied Math 9 May 8th, 2009 12:02 PM cos5000 Number Theory 4 April 28th, 2008 10:36 AM MaD_GirL Number Theory 5 November 14th, 2007 06:34 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top