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Thread: quick question

  1. October 22nd 2009, 12:57 PM #1
    brogers
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    quick question

    Hi, I'm new here. Just a quick question

    Is there a theorem that states that if gcd(a,m)=1 and a^x \equiv a^y (mod m), then a^{x-y} \equiv 1(mod m)?
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  2. October 22nd 2009, 01:34 PM #2
    proscientia
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    I don’t know if there is a name for this theorem, but the result can be quite easily established by considering the multiplicative group of the units of the ring \mathbb Z_m.
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  3. October 22nd 2009, 01:43 PM #3
    brogers
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    thanks, I just needed to know if that was a real theorem
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