Does $\mathop{\LARGEΣ}_{k = 1}^{n}k^α = \left(\mathop{\LARGEΣ}_{k = 1}^{n}k\right)^β$ for which $α \neq 3, \ β \neq 2$ and $α \neq β$?
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
39646
Is there a relation between $\rho(A) + \rho(B)$ and $\rho(A+B)$, where $\rho$ is the spectral radius?
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
11389
What is $\lim_{n\to \infty}\sum_{k=1}^n \left(\frac{k}{n}\right)^n$?
32760
Is $\mathbf{Q}(\sqrt{2}, \sqrt{3}) = \mathbf{Q}(\sqrt{2}+\sqrt{3})$?
128710
Prove that $\langle a^n \rangle \bigcap \langle a^k \rangle = \langle a^{lcm (n,k)} \rangle$
97720
Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
29578
Why is $\binom{2n}{n} \asymp \Theta \big(\frac{2^{2n}}{\sqrt{n}}\big)$?
142256
Polygamma function series: $\sum_{k=1}^{\infty }\left(\Psi^{(1)}(k)\right)^2$
104034
Is $\le$ defined by $\langle 𝑥_1, 𝑦_1 \rangle \le \langle 𝑥_2, 𝑦_2 \rangle$, if $𝑥_1 \le 𝑥_2 \land𝑦_1 \ge 𝑦_2$ a linear order?
60665
Meaning of $\mathbb{Z}\left[\sqrt{3}\right]$?
129732
What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
20299
Is $k=3$ the only solution to $\sum_{r=1}^n r^k =\left( \sum_{r=1}^nr^1 \right)^2 $?
97583
Let $\alpha, \beta, \gamma$ be cardinals, $\beta \leq \gamma$, prove $\alpha ^{\beta}\le \alpha ^{\gamma}$
11935
Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
68858
Prove that $\prod_{n=2}^∞ \left( 1 - \frac{1}{n^4} \right) = \frac{e^π - e^{-π}}{8π}$
3735
If $\sum_{1}^{\infty}(a_n)^3$ diverges, does $\sum_{1}^{\infty}(a_n)$?