Need help in showing that if (a,b) = 1, then (n,ab) = (n,a)(n,b).
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
3301
If $AB = I$ then $BA = I$
63267
Under what conditions on the sets $A$ and $B$ will it be true that $A\times B= B\times A$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
49143
Showing $A \subset B \iff A\cap B=A$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
111003
Prove that if $A\triangle B = C\triangle B$, then $A = C$
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
124742
P(A|C)=P(A|B)*P(B|C)?
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$