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Question about proof

  1. Sep 28, 2009 #1
    prove Byron's Conjecture. Define the set
    Znx={k∈Zn but not including zero :gcd(k; n) = 1}
    (a) Prove that Znx is a group under multiplication (mod n).
    (b) Prove that an element a∈Zn is invertible in Zn (with respect to multiplication (mod n)) if and only if a∈Znx

    Znx x should be above n . i dont know how to type
  2. jcsd
  3. Oct 1, 2009 #2


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    What's the question?
  4. Oct 1, 2009 #3
    Use the fact that you can write out ak + bn = 1 for some integers a,b to show the elements are invertible.
  5. Oct 2, 2009 #4
    LaTeX: [itex]\mathbb{Z}_n^{\times}[/itex] ... use the "Quote" button to see it.
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