If $m$ is a divisor of $k$ and $n$ is a divisor of $k$ and $m$ and $n$ prime to each other then $mn$ is divisor of $k$.
54699
Product of pairwise coprime integers divides $b$ if each integer divides $b$
62474
If $AB=I_n$ and $BA=I_m$ then $n=m$.
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
99376
Prove that If $m'$ is a common multiple of $s$ and $t$, then $m | m'$. Here $m$ is the LCM of $s$ and $t$.
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
82071
divisor of a product of integers is a product of divisors
81778
If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)
46383
If $x$ divides $z$, $y$ divides $z$ and $x$ and $y$ are relatively prime, then $xy$ divides $z$.