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RE: [PrimeNumbers] reduced residue systems question please help

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  • Jon Perry
    Woh! Steady on, Jon. You re _way_ off base here. 2 is not coprime to 30. gcd(2,30)=2 3 is not coprime to 30. gcd(3,30)=3 5 is not coprime to 30. gcd(5,30)=5 1
    Message 1 of 5 , Mar 1, 2003
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      'Woh! Steady on, Jon. You're _way_ off base here.

      2 is not coprime to 30. gcd(2,30)=2
      3 is not coprime to 30. gcd(3,30)=3
      5 is not coprime to 30. gcd(5,30)=5

      1 is coprime to 30. gcd(1,30)=1

      |{1,7,11,13,17,19,23,29}| = 8 as correctly stated by Liu.'

      Correct. As the whole page in question
      (http://www.primepuzzles.net/problems/prob_037.htm) is completely littered
      with typos and misleading nomenclature, I don't feel completely aggrieved at
      having made such a simple error.

      As to what 'Tn mod mn is equivalent to the class of residues
      Tn+<0,1,2,...,pn=1>*<mn> mod m[n+1]'

      means, it should read:

      T_n mod m_n is equivalent to the class of residues
      Tn+(<0,1,2,...,pn-1>*<mn>) mod m_(n+1)

      which comes clear if you look at the examples, except for m_n is incorrectly
      defined.

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry/maths/
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    • velozant <velozant@msu.edu>
      Thanks a lot for your responses. What I am confused about is that I don t understand how adding * to Tn makes it equivalent mod m[n+1].
      Message 2 of 5 , Mar 1, 2003
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        Thanks a lot for your responses. What I am confused about is that I
        don't understand how adding <0,1,2,...,pn-1>*<mn> to Tn makes it
        equivalent mod m[n+1]. What I would like is a theorem like the one
        that one can uset to prove that if (k,S)=1 and S is a reduced
        residue system then so is k*S. I think it should be obvious since
        most people accept it and I see from examples that it is true, but I
        just want to know what theorem he is using to imply this equivalence
        or if it follows directly from the definition of Tn. Any help will
        be greatly appreciated.
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