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November 29th, 2012, 05:14 PM   #1
unm
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Modulo Residue problem

Hello All,

I am stuck with this problem.

How can I prove the series {kb( mod d)}, k = 1, 2, . . . , d contains d different residues

Can anyone please help me in this regard.

I will be grateful.

Thank you
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November 30th, 2012, 09:39 PM   #2
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Re: Modulo Residue problem

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Originally Posted by unm
How can I prove the series {kb( mod d)}, k = 1, 2, . . . , d contains d different residues
Is b arbitrary? If so then this is false unless d is prime. For example with d = 6 and b = 2, as k goes from 1 to 6, kb is the set {2,4,6,8,10,12} which only has three different residues mod 6, namely {2,4,0}.
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December 1st, 2012, 05:26 AM   #3
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Re: Modulo Residue problem

The condition you really need is gcd(b, d) = 1, since b = 0, d prime also fails.
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December 1st, 2012, 09:57 AM   #4
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Re: Modulo Residue problem

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Originally Posted by CRGreathouse
The condition you really need is gcd(b, d) = 1, since b = 0, d prime also fails.
Oops yes of course ... don't know how I missed that. Thanks for the correction.
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December 1st, 2012, 05:42 PM   #5
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Re: Modulo Residue problem

@ Maschke and CRGeathouse..

Thanks for the comments..

Yes i was missing the statement of gcd(d,b) = 1.
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