If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
16023
Are associates unit multiples in a commutative ring with $1$?
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
91829
Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
26861
$a+b=c \times d$ and $a\times b = c + d$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
145719
Similarity between $A$ and $B (2\times 2)$.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?