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August 31st, 2010, 11:29 AM  #1 
Newbie Joined: May 2007 Posts: 18 Thanks: 0  Cyclical Permutation Problem
Hey guys! Can one of you help me with the following problem? Prove that if a number of n digits, expressed in the scale of r, is divisible by any factor of r^[n1], that divisibility is not altered by a cyclical permutation of the digits of the original number. Thank! 
August 31st, 2010, 01:40 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Cyclical Permutation Problem Hello, morning_mood! Please check the wording of the problem. As stated, the claim is not true. Quote:
[color=beige]. . . . . . . . . . . . . . [/color][color=red]? ? ?[/color]  
August 31st, 2010, 04:31 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Cyclical Permutation Problem
I'm guessing it should be r^n  1, not r^(n  1).

August 31st, 2010, 07:49 PM  #4 
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Cyclical Permutation Problem The problem is similar to a phenomenon in baseten. If a number is divisible by 9, then any cyclic permutation [color=beige]. . [/color] of the digits of is also divisible by 9. 
September 1st, 2010, 04:29 AM  #5 
Newbie Joined: May 2007 Posts: 18 Thanks: 0  Re: Cyclical Permutation Problem
You guys are right, it should have been r^1  1. I got confused about how write powers here and reported the problem incorrectly. Thanks for the help! 

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