Question

prove that the ring of gaussian In-
tegers is an
Euclidian ring​

Answer 1

Theorem. The ring Z[i] of Gaussian integers is an Euclidean domain. ... The other thing we need to establish to complete the proof of the fact that Z[i] is an Euclidean domain is that for any x, y ∈Z[i], there exist q, r ∈Z[i] such that y = qx + r with r = 0 or d(r) < d(x).

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