$(a,n)=1\Rightarrow \exists [b]\in J_n $ such that $[a][b]=1$
32108
$ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
120094
Prove, that for any A, B, C sets, $A\times (B\setminus C) = (A\times B)\setminus (A\times C)$ is true.
39563
How to show $a,b$ coprime to $n\Rightarrow ab$ coprime to $n$?
107765
Prove that there exists two roots in $[-1,1]$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
93771
Prove that for any set $A$ there is some $x \notin A$
76790
Condition to guarantee $f=0$ on $[a,b]$
30694
Show that there exist $[a,b]\subset [0,1]$, such that $\int_{a}^{b}f(x)dx$ = $\int_{a}^{b}g(x)dx$ = $\frac{1}{2}$
108740
$C^1[a,b]$ is closed in $C[a,b]$
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
6896
If $A/I \cong A/J$ as rings and $I\subseteq J,$ then $I=J.$
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
77510
$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$
12301
Show that $\lim_{n \rightarrow \infty} \sqrt[n]{a} =1$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$