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Rather basic question - I think

  1. Nov 4, 2004 #1
    If a and N coprime, a < N and r is even how can

    a^(r) = 1 mod(N) be written as


    a^(r) - 1 = 0 mod(N) ?

    I don't know much number theory (I'm a physics student)

    Thanks
     
  2. jcsd
  3. Nov 4, 2004 #2

    shmoe

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    Science Advisor
    Homework Helper

    Hi, the conditions you list at the start don't matter for what you've just asked (a, N coprime, etc). For any a,b, and N,

    a=b mod (N)

    if and only if

    N divides a-b

    if and only if

    N divides (a-b)-0

    if and only if

    a-b=0 mod(N)


    Working mod N you can add, subtract and multiply as normal (division isn't always possible!), you just have the luxury of reducing things mod(N) afterwards.
     
  4. Nov 4, 2004 #3
    ahh i see what you did there.. thanks!
     
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