$B \equiv 1$ or $-1$ (mod n) where $B$ is the product of the elements of $U_n$.
129827
Product of invertibles in $\Bbb Z_n$ [Wilson's Theorem generalization]
127816
Number theory proof mod p
124279
$g^k$ is a primitive element modulo $m$ iff $\gcd (k,\varphi(m))=1$
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
84
For what $n$ is $U_n$ cyclic?
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
63359
Show that the product of all group elements is $e$ or $u$ if $G$ has exactly one involution $u$
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
132587
Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
84789
Order of products of elements in a finite Abelian group