Prove that there exist integers $k, l \in \mathbb{N}$ such that $\mathrm{ord}(x^ky^l) = \mathrm{lcm}(\mathrm{ord}(x), \mathrm{ord}(y))$
9393
Order of elements is lcm-closed in abelian groups
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
128634
Doubt related to a theorem in congruences of Chapter 5 of Apostol Introduction to analytic number theory
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
131754
Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
2626
Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$
148108
Let $L=\operatorname{lcm}(o(a), o(b))$ and prove that $(ab)^L =e$.
32965
Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
50396
How can I show that $ab \sim \gcd (a,b) {\operatorname{lcm} (a,b)}$ for any $a,b \in R \setminus \{0\}$?