# quick question

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• Oct 22nd 2009, 01:57 PM
brogers
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 $a^{x-y} \equiv 1(mod m)$?
• Oct 22nd 2009, 02:34 PM
proscientia
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 $\mathbb Z_m.$
• Oct 22nd 2009, 02:43 PM
brogers
thanks, I just needed to know if that was a real theorem