November 19th, 2013, 03:41 PM  #1 
Newbie Joined: Oct 2013 Posts: 25 Thanks: 0  Primitive root
p prime, If p=1 ( mod 3) then Zp contains primitive cube roots of unity. Now I am considering which p does Zp contains primitive fourth roots of unity. I can prove that if Zp contains primitive fourth roots of unity, then 4(p1) . but how about the opposite way? I mean if p=1(mod4) then Zp contains primitive fourth roots of unity?? I know this statements true if q prime instead of 4. And what values of p does Zp contains primitive fourth roots of unity??? 
November 19th, 2013, 08:47 PM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Primitive root Quote:
 

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