Prove if $n\in N$ is composite then there exists an equivalence class $a\bmod n$ that does not have a multiplicative inverse
35034
Multiplicative inverses for $Z_n$
49166
$R^n \cong R^m$ iff $n=m$
110018
Conjugacy classes in $A_n$.
70861
$\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
52429
Explicit countable elementary extension of $\mathbb{N}$
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
55018
Prove that $A^*A + I$ is invertible
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
93952
Show that $X$ can be represented as a union of disjoint equivalence classes
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
88645
Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$