Prove that if $a_{2n} \rightarrow g$ and $a_{2n+1} \rightarrow g$ then $a_n \rightarrow g$
74542
Convergence of a sequence whose even and odd subsequences converge
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
133915
In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
65096
$\chi(G)+\chi(G')\leq n+1$
31347
$A_n$ is generated by 3-cycles given $n\geq 3$. Is this proof correct?
89175
Proof of $(a+b)^{n+1}$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
86823
proof verification: If $f:G \rightarrow H$ is group homomorphism, and $H$ is abelian, then $G$ is abelian
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
98816
How to prove that $\{f+g<a\}=\bigcup_{r\in{\Bbb Q}}(\{f<r\}\cap\{g<a-r\})$?
152132
Proving if $\lim_{n\rightarrow\infty}a_n=L $ then $\lim_{n\rightarrow\infty} \frac{a_1+a_2+\cdots+a_n}n=L $
1275
Prove that $a_1+\cdots+a_n \geq n$ if $a_1$, $a_2$, ... $a_n$ are positive real numbers and their product is $1$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic