Prove that if $A|B$ and $B|A$, then $A=B$?
30583
If $a\mid b$ and $b\mid a$, $a,b\in R$, show that $\exists w \in R^\times$ with $b=wa$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
158845
Given $A$ and $B$ positive-definite matrices and $Q$ unitary matrix, prove that if $A = BQ$, then $A=B$.
14162
How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$
13074
Prove Logical Equivalence
13026
Prove that if AB=I_m, then rk(A)=rk(B).
158695
Prove that if $AB$ is invertible then $B$ is invertible.
145397
How to prove that for every $i$, $a_i = i$
136835
ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
24856
Proving sup(A + B) = sup A + sup B