prove that if $(\mathbb{Z}/n\mathbb{Z})^{*}$ is cyclic, $n=2,4 $~or~$ p^k, 2p^k$ where $p$ is an odd prime number.
84
For what $n$ is $U_n$ cyclic?
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
28362
Product of two cyclic groups is cyclic iff their orders are co-prime
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
121874
Use Induction to prove that for all $n \in \mathbb{N}, (x^n + \frac{1}{x^n}) \in \mathbb{Z}$ if $x+\frac{1}{x}\in\mathbb{Z}$.
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
16559
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
69046
Proof of $\mathbb{Q}$ is not cyclic
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.