My Math Forum Order of the residue classes

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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^{'}
 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: Thanks from heinsbergrelatz
 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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