Does $a$ divide $c$ if $a$ divides $b$ and $b$ divides $c$?
56512
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
17316
If $a^\phi = 1$ then the order of $a$ divides $\phi$
58579
Can't understand a proof: Let $a,b,c$ be integers. If $a$ and $b$ divide $c$, then $lcm(a,b)$ also divides $c$
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
55437
When does $2^{n}$ divide $3^{n}-1$
71299
Prove that $\frac{a}{b} < \frac{a+c}{b+d} <\frac{ c}{d}$
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
106319
Can we divide two vectors?
97667
If $a<b$, $c<d$ then $a+c<b+d$?
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
7894
Does it follow that $(n!)^n$ divide $(n^2)!$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
139018
A does the same B as does C
1448
$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$