Common divisor of $a+b$ and $ab$.
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
45979
Deﬁne a new addition ⊕ and multiplication on Z by a⊕b = a + b−1 and ab = a + b−ab.
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
18528
Show that $a \star b=a \cdot b+a+b$ is binary operation for the group $\Bbb{ Q} \setminus \{-1\}$
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$
39563
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
6096
If $A+B=AB$ then $AB=BA$
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
27250
Greatest common divisor of two relatively primes
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$