If $N(z)=a^2+b^2 =\text{ prime } \in \Bbb{Z}$ show $\Bbb{Z}[i]/(a+bi)$ is a field of prime order.
54585
Order of some quotient ring of Gaussian integers
55429
Why does a Galois field have to have an order of $p^n$ where $p$ is prime?
74631
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
123419
Abstract algebra: homomorphism and an element of a prime order
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
133561
show that if $K$ is a field then $K[x]$ is principal
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
71608
A property of finite field of order $2^n$
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
148118
Prove that field of complex numbers cannot be equipped with an order relation
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$