Existence of $p \times p $ matrices $A$ and $B$ over the field $\mathbb F_p$, $p$ prime, such that $AB-BA=I$.
125647
Solutions to the matrix equation $\mathbf{AB-BA=I}$ over general fields
38419
Existence of Polynomial with whom product contains only prime powers
46110
how many 2x2 matrices are invertible in mod p
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
123726
$2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
84626
Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
81221
The prime number theorem over a finite field - Lang's *Algebra*, Chapter V, Exercise 23(b)
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
64077
$I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
78298
On the nilpotence of the matrix $AB-BA$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
128652
Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$