Example Galois Group Primitive Root

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  1. Harpreet Bedi
  2. Cyclotomic Polynomial
  3. Galois Group
  4. Mathematics (Field Of Study)
  5. Évariste Galois (Academic)
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Very helpful among all videos available on YouTube

kajalmittal
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You took <2> as a generator and I see that you could have taken any of the numbers as a generator as 13 is prime and so every number in Z/13Z is relatively prime to 13. At about 5 minutes though you take (zeta^2)^k where k is a multiple of a particular divisor for the associated subgroup. I am guessing that you could have taken any <3>, <4> .. <12> as generators (sure <12> = <-1> etc.) and somehow gotten the same answers as you did as when <2> was chosen as a generator. So for example, how would one show that combining the sum of (zeta^5)^k = sum of (zeta^2)^k for k a multiple of a particular divisor? Thanks, and a huge thanks for posting these Harpreet! I am a huge fan!

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