Number Theory: Prove that $m | \phi(a^m - 1)$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
91889
Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.
125188
how to prove $m^{\phi(n)}+n^{\phi(m)}\equiv 1 \pmod{mn}$ where m and n are relatively prime?
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
144819
Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
68705
Prove that $A\ge0, B\ge0$ and $A\ge B$ implies $B^{-1}\ge A^{-1}$
106401
Prove: $p-mq | f(m)$ where $m$ is any integer
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 $m, n$.
110826
prove that : $ i = \sqrt {-1}\ $
41141
Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer.
89175
Proof of $(a+b)^{n+1}$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$