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 November 29th, 2012, 04:14 PM #1 Newbie   Joined: Nov 2012 Posts: 25 Thanks: 0 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
November 30th, 2012, 08:39 PM   #2
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Re: Modulo Residue problem

Quote:
 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}.

 December 1st, 2012, 04:26 AM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Modulo Residue problem The condition you really need is gcd(b, d) = 1, since b = 0, d prime also fails.
December 1st, 2012, 08:57 AM   #4
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Re: Modulo Residue problem

Quote:
 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.

 December 1st, 2012, 04:42 PM #5 Newbie   Joined: Nov 2012 Posts: 25 Thanks: 0 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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### Prove that the series {kb (mod d)}, k = 1, 2, ..., contains d different residues

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