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Homework Help: Number proof

  1. Jun 2, 2009 #1
    1. The problem statement, all variables and given/known data

    I need to prove that if b is coprime to 6, then b^2 is congruent to 1 (mod 24)

    2. Relevant equations



    3. The attempt at a solution

    I know that this means the gcd(b,6)=1

    Any help though to start this question off would be great thanks.
     
  2. jcsd
  3. Jun 2, 2009 #2

    HallsofIvy

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    Science Advisor

    And gcd(b, 6)= 1 means b must not have 2 or 3 as factors.
     
  4. Jun 2, 2009 #3
    If gcd(b,6) = 1 then b = r (mod 6) for only two values of r between 0 and 5. Then we can write b = 6*n + r for some integer n and look at the expansion of (6*n + r)^2.
     
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