Φ(mn) = Φ{ (m, n)Φ[m, n] } ∀ m,n ∈ ℕ
37346
If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$.
135694
Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
133884
A proof using Yoneda lemma
19599
$ d(x_n,y_n) \to d(x,y)$ if $x_n\to x$ and $y_n \to y$
39453
How do I prove that $S^n$ is homeomorphic to $S^m \Rightarrow m=n$?
36747
$\text{Tor}_0^R(M,N)\simeq M\otimes_R N$
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
115258
Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.
119118
Prove $n\mid \phi(2^n-1)$
120629
Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
117681
For which Natural $n\ge2: \phi(n)=n/2$
37928
Isomorphism between $D_{2n}/Z(D_{2n})$ and $D_n$
124844
Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$