Prove that exactly $\phi(d)$ elements have order $d$
104549
When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
144394
Order 2 elements in finite characteristic field
5089
An element of a group has the same order as its inverse
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
98514
Prove by induction that the number of derangements of length $n$ is $D_n = (n-1)(D_{n-1}+D_{n-2}), n>2$
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
82878
Order of cyclic groups and the Euler phi function
158282
Finite order of an element $f(g)$ of a homomorphism $f$
26233
$[K(\zeta_n):K]=\phi(n)$?
120629
Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
76292
Showing that $f$ is identically $0$ on $\mathbb{D}$
131946
Order of an Element Under a Homomorphism
26658
A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
8742
Examples and further results about the order of the product of two elements in a group
84789
Order of products of elements in a finite Abelian group
4530
For which natural numbers are $\phi(n)=2$?