$\forall A,B \in M_n(\mathbb F),AB=BA,\exists C \in M_n(\mathbb F),f(x),g(x)\in \mathbb F[x],A=f(C),B=g(C)?$
57731
Can commuting matrices $X,Y$ always be written as polynomials of some matrix $A$?
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
76148
Show that $\exists c \in \mathbb{R} : f(c) = 0$
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
103019
Find all functoins $f: \mathbb R \rightarrow \mathbb R$ such that $\forall x,y \in \mathbb R f(xy+f(x))=xf(y)+f(x)$
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
109498
Linear maps $f: M_n \longrightarrow \mathbb{R}$ such that $f(AB) = f(BA)$