$AB-BA$ invertible and $A^2+B^2 = AB$ then $3$ divides $n$
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
124734
If $A^3=O$ is the matrice $A^2-A+I$ invertible?
89184
Prove $30|(a^3b-ab^3) $
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
3301
If $AB = I$ then $BA = I$
76017
Prove that $x^3-2$ and $x^3-3$ are irreducible over $\Bbb{Q}(i)$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$