To show $|(\mathbb{Z}/n\mathbb{Z})^{\times}| = \varphi(n)$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
49953
Proving that a function from $N\times N$ to $N$ is bijective.
151111
How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
54406
Is $\mathbb Q \times \mathbb Q $ a denumerable set?
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
114916
$\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
146990
How to find the number of automorphisms on $\mathbb Z_2\times \mathbb Z_4$
122312
How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
109596
Isomorphism from $\mathrm{Aut}(\mathbb{Z}/2\mathbb{Z}\times \mathbb{Z}/2\mathbb{Z})$ to $S_3$
20581
How to show that $\Gamma\vdash (\varphi\to\neg\varphi)\to\varphi$?
5577
If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module.