Prove that for any integers $m$ and $n$ we have to: $mn=(m,\,n)[m,\,n]$.
21288
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
75614
Proving that $n|m\implies f_n|f_m$
91451
find all positive integer $m,n$
127855
Show that the product of any $m$ consecutive positive integers is divisible by $m!$
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
114404
For which positive integer values of $n$ does $a|mn-b?$
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
34929
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$