Given that 3 is a primitive root modulo 17, determine all solutions to the congruence Since 3 is a primitive root we have: and so I am not sure how to progress on from here... cheers for any help!
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Originally Posted by usagi_killer Given that 3 is a primitive root modulo 17, determine all solutions to the congruence Since 3 is a primitive root we have: and so I am not sure how to progress on from here... cheers for any help! We work modulo 17 in the following: ... Tonio
ohh thanks very much, i actually just figured out another method, is this correct? Thus So the solution is Is this valid? Cheers!
Originally Posted by usagi_killer Given that 3 is a primitive root modulo 17, determine all solutions to the congruence Since 3 is a primitive root we have: and so I am not sure how to progress on from here... cheers for any help! Multiplying the congruence by we get, equivalently, . There exists a positive integer such that and so . Finally, , which is equivalent to solving . The solution in the range is . The solutions of the original congruence are given by .
Last edited by melese; March 23rd 2011 at 08:12 AM. Reason: It should be 3^3 - usagi_killer corrected me.
Originally Posted by melese Multiplying the congruence by we get, equivalently, . There exists a positive integer such that and so . Finally, , which is equivalent to solving . The solution in the range is . The solutions of the original congruence are given by . Thanks heaps for the help! But for the last congruence you mean right? :P
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