Using that the Eisenstein integers $\mathbb{Z}[w]$ where $w^2+w+1=0$ are UFD (unique factorisation domain) show that any prime p where $p=1$ mod 6, we can write $p=3a^2+b^2$ for integers $a$ and $b$.
#Show p=3a^2+b^2 if p=1 mod 6, using Eisenstein integers. Please help!
rocky spindle
modest latchBOT
Using that the Eisenstein integers $\mathbb{Z}[w]$ where $w^2+w+1=0$ are UFD (un...
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borekking
rocky spindle
Using the norm $N(a+bw) = (a+bw)(a+bw^2) = a^2-ab+b^2$ we can easily show that $p=a^2-ab+b^2$ but I cannot find any suitable transformation from there