Let a, b, an m be integers. If a and b are relatively prime and a|m and b|m, then ab|m.
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
77070
Prove Euler's Theorem when the integers are not relatively prime
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
155929
Let $A, B$ be sets. Show that $\mathcal P(A ∩ B) = \mathcal P(A) ∩ \mathcal P(B)$.
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
89066
Find all integers less than $m$ that are relatively prime to it
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
138707
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
2884
$m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?