Is there an elementary proof that $n \mid \phi(p^n-1)$?
88662
$n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
68385
Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $
61858
Is there $\phi(n)=n/6$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
18140
When does $\,n\mid q^3 \Rightarrow n\mid q\,$?
88656
For $p$ prime, show that $\Phi_{p^n}(x) = 1 + x^{p^{n-1}} + x^{2p^{n-2}} + \dots +x^{(p-1)^{p^n-1}}$
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
136077
Prove that $x-1$ is a factor of $x^n-1$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
26233
$[K(\zeta_n):K]=\phi(n)$?