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August 31st, 2010, 11:29 AM   #1
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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^[n-1], that divisibility is not altered by a cyclical permutation of the digits of the original number.

Thank!
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August 31st, 2010, 01:40 PM   #2
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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]

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August 31st, 2010, 04:31 PM   #3
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Re: Cyclical Permutation Problem

I'm guessing it should be r^n - 1, not r^(n - 1).
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August 31st, 2010, 07:49 PM   #4
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Re: Cyclical Permutation Problem


The problem is similar to a phenomenon in base-ten.

If a number is divisible by 9, then any cyclic permutation
[color=beige]. . [/color] of the digits of is also divisible by 9.

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September 1st, 2010, 04:29 AM   #5
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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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