In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as Z[i]. This integral domain is a particular case of a commutative ring of quadratic integers. It does not have a total ordering that respects arithmetic.
== Formal definition ==
Formally, the Gaussian integers are the set
Z
[
i
]
=
{
a
+
b
i
...
I am not sure what is the right phrase for primes in some ring. The definition I was gave is that in a ring $A$, $p\in A$ is prime if $\forall x,y \in A$ such that $p\mid xy$, $p\mid x$ or $p\mid y$.
I don't know how to start.(I arrived at odd expressions but too long ones) and it is complex fo...
