Proving $A \cong C$ if $A \cong B$ and $B\cong C$.
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
99376
Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
49166
$R^n \cong R^m$ iff $n=m$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
15184
$C \otimes A \cong C \otimes B$ does not imply $A \cong B$
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
110944
Proving that $AB-BA=cI$ for nontrivial $c \in \mathbb{C}$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
158355
If $A$ commutes with $B$ and $B$ commutes with $C$, then $A$ commutes with $C$