When does $a\mid c$ and $b\mid c$ imply $ab\mid c$?
102980
finding all numbers $a,b$ that divide $c$ but product of $a$ and $b$ does not divide $c$
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
17677
Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
5149
Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $
105233
Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
92975
Does $a^n \mid b^n$ imply $a\mid b$?