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Oct 5, 2010 at 6:05 comment added Gerry Myerson Oops, I meant $3+\zeta_3$ and $3+\zeta_3^2$, whose product is 7.
Oct 5, 2010 at 4:34 comment added Cam McLeman (but good answer).
Oct 5, 2010 at 4:19 comment added Cam McLeman I don't think your factorization of 7 is correct. In particular, $N(3-\zeta)=(3-\zeta)(3-\zeta^2)=9+3+1=13$.
Oct 5, 2010 at 4:03 history answered Gerry Myerson CC BY-SA 2.5