It is known that a polynomial x^2 +x +1= 0 has a solution in Zp if and only if -3 is a square root in Zp, which is if and only if p=1.mod 6. the splitting field Zp(y1) where y1 is a solution of the polynomial x^2 +x +1= 0 . gle.com/d/optout <https://groups.google.com/d/optout>.
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