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November 19th, 2013, 03:41 PM   #1
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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|(p-1) . 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???
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November 19th, 2013, 08:47 PM   #2
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Re: Primitive root

Quote:
Originally Posted by James1973
if p=1(mod4) then Zp contains primitive fourth roots of unity?
Yes, and the same holds for the if-and-only-if statement.
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