Is there a known necessary and sufficient criterion for a Gaussian Integer $a+ib$ to be prime in $\mathbb{Z}[i]$?
140550
Irreducible element iff prime norm in Gaussian integers?
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
126017
Entire function having simple zero at the Gaussian integers
41878
Cardinal of quotient rings of gaussian integers.
39698
On uniqueness of sums of prime powers
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
54585
Order of some quotient ring of Gaussian integers
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
111898
Is $\{ (e^{2\pi i a n},e^{2\pi i b n }) : n \in \mathbb{Z} \}$ dense in the torus, where $a,b$ irrationals such that $a/b$ irrational?
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
48405
Why does the characteristic of a finite field always have to be prime?
157652
Fermat's Last Theorem for Gaussian Integers (excluding the integers or  same pure imaginaries)
150677
What are the integers $n$ such that $\mathbb{Z}[\sqrt{n}]$ is integrally closed?
76807
How come if $\ i\ $ not of the following form, then $12i + 5$ must be prime?
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
126471
At least one prime between $\sqrt{n}$ and $n$?
138459
Norm and Algebraic Integers