There are infinitely many integers $n$ such that $\varphi(n)=n/3$
53745
Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$
94575
Inductive proof that there are infinitely many pairs of consecutive powerful integers?
115258
Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.
53525
Infiniteness of non-twin primes.
106111
Understanding that there are infinitely many primes of form $4n+3$
91356
Irreducibility of an infinite sequence of polynomials
35326
There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
52565
Prove that if $d \mid n \in \mathbb{N}$, then $\varphi(d) \mid \varphi(n)$.
61858
Is there $\phi(n)=n/6$
47211
Does $\varphi(x)\le\int_0^x\varphi(t)dt$ for all $x\in[0,\infty)$ imply $\varphi\equiv0$.
22084
$\mathbb{Z}[i] / (2+3i)$ has 13 elements
67295
Please check my proof for $N$ is infinite
137711
Alternative proof that $[\Bbb{Q}(\zeta_n) : \Bbb{Q} ]= \varphi(n)$ uses circular reasoning?
33786
Proof that a certain fraction is always an integer
12436
The cardinality of the set of all finite subsets of an infinite set
2882
Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?