This question already has an answer here: Norm-Euclidean rings? 2 answers

I’m having some trouble proving that the Gaussian Integer’s ring ($\mathbb{Z}[ i ]$) is an Euclidean domain. Here is what i’ve got so far. To be a Euclidean domain means that there is a defined application (often called norm) that verifies this two conditions: $\forall a, b \in \mathbb{Z}[i] \backslash {0} \hspace{2 mm} a \mid […]

Intereting Posts

All solutions to the vector equation Ax = v + w given A's eigenvalues and eigenvectors
Solution to General Linear SDE
When to learn category theory?
Prove that if $p$,$q$ and $\sqrt{2}p+\sqrt{3}q$ are rational numbers then $p=q=0$
Structure Theorem for abelian torsion groups that are not finitely generated
To get addition formula of $\tan (x)$ via analytic methods
How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
Solving recurrence relation?
Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$
Irreducible solvable equation of prime degree
Intersection of Connected Sets
Can there be two distinct, continuous functions that are equal at all rationals?
Inverse of this $3$-by-$3$ matrix using the Cayley–Hamilton theorem
What is the definition of tensor contraction?
probability, random walk, Markov chain question