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October 25th, 2017, 10:12 AM  #1 
Newbie Joined: Oct 2017 From: sweden Posts: 20 Thanks: 0  Order of the residue classes
There is one problem I can't solve for the particular section under prime power modulus in my textbook, and it's this: If the reduced residue classes $a$ and $b \,($mod $p$) both have order $3^j,$ how can I show that the two residue classes $ab$ and $ab^2$ one of them has order $3^j$ and the other $3^{j^{'}},$ where $p$ is prime and $j>0$, for $j^{'}<j$ ? How could I show this? Could anyone help me please? Last edited by skipjack; October 25th, 2017 at 10:50 AM. 
October 26th, 2017, 04:49 PM  #2 
Member Joined: Jan 2016 From: Athens, OH Posts: 89 Thanks: 47 
Your problem is really one about finite cyclic groups. For a prime p, the integers modulo a power of p have a primitive root; i.e. the underlying group is cyclic. Here's your problem restated: 
November 4th, 2017, 06:11 AM  #3 
Newbie Joined: Oct 2017 From: sweden Posts: 20 Thanks: 0 
Thank you very much !


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