Eisenstein integer

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In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known^[1] as Eulerian integers (after Leonhard Euler), are the complex numbers of the form

${\displaystyle z=a+b\omega ,}$

where a and b are integers and

${\displaystyle \omega ={\frac {-1+i{\sqrt {3}}}{2}}=e^{i2\pi /3}}$

is a primitive (hence non-real) cube root of unity.

The Eisenstein integers form a triangular lattice in the complex plane, in contrast with the Gaussian integers, which form a square lattice in the complex plane. The Eisenstein integers are a countably infinite set.