Hi,


I have a finite field Fp with p = 11 mod(12) and I am trying to get the third nontrivial root of unity in Fp^2 = Fp^2[x]/(x^2+1). So, i need x where x^3=1.


Somehow I came into a source saying that it would be:
(p-1)/2 + (3^((p+1)/4)) mod(p))\*i where i^2=-1.
But it seems not to be correct:
Any idea?



nontrivial cube root of unity
OK, this is about imitating the formula for a complex cube root of unity. Write p as 12k - 1. The real issue is only why 3 to the power 3k should act as square root of 3 in this field. Square it and apply Fermat's little theorem to see why. (There is a missing factor 2 in the formula you gave.)


