Show that $(a!)^b b! \mid (ab)! $
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
120573
Does $a!b!$ always divide $(a+b)!$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
66946
show that $(i+k)! > i!k!$ algebraically
58589
On the factorial equations $A! B! =C!$ and $A!B!C! = D!$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
50266
In the following figure prove that: $AK||BC$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
50614
If $4\mid a+bc$ and $6\mid b+ac$ prove that $2\mid a^2-b^2$
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$