Suppose n is a product of distinct odd primes. Show $a^{\phi(n)+1}\equiv a $ (mod $n$).
49938
Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
6453
Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
54554
If a product of relatively prime integers is an $n$th power, then each is an $n$th power
54359
Odd Primes Problem Proof
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
127816
Number theory proof mod p
114796
Direct proof that the product of odd integers is odd
144851
For a prime $p \equiv 1$ or $3$ (mod $8$), show that the equation $x^{2} + 2y^{2} = p$ has a solution.
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.
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
6160
How to prove a number $a$ is quadratic residue modulo $n$?
52530
There exists a prime congruent to $m$ mod $p$
157711
Number Theory: Prove that $m | \phi(a^m - 1)$