$P=\sum_{k=0}^{n}c_{k}z^{k}$ if $\forall t\in[k].c_t\in\mathbb{R}\rightarrow\int_{-1}^{1}P^2\leq\pi\sum_{k=0}^{n}c_{k}^{2}$
5430
Using Cauchy's integral theorem to prove a inequality
56928
$\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$
48642
Let $f(n) = \sum_{(k,n)=1} e^\frac{2\pi ik}{n}$. Show that $f(n) = \sum_{k=1}^{n}\left(\sum_{d\mid (k,n)} \mu(d)e^{\frac{2\pi ik}{n}} \right) $
30953
Is $\sum_{k=1}^{n} \sin(k^2)$ bounded by a constant $M$?
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
53244
Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
36639
Prove by induction that $\sum_{r=0}^{n}\begin{pmatrix}n \\ r \end{pmatrix}=2^k$
97119
Prove that $\prod_{i=1}^n(1+x_i)\leq \sum_{i=0}^n\frac{S^i}{i!}$, where $x_i\in\mathbb{R^+}$.
35525
Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula
41876
Finding an asymptotic for the sum $\sum_{p\leq x}p^m$
75227
If $S=\{1,2,\dots,n\}$ and $P_n(k)$ be the number of permutations of $S$ having $k$ fixed points, then $\sum_{k=0}^nk.P_{n}(k)=n!$
133505
Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$
126073
Radius of convergence of power series $\sum c_n x^{2n}$ and $\sum c_n x^{n^2}$
76828
Evaluating $\sum_{i = 0}^{\lfloor n/2 \rfloor} {n \choose 2i}p^{2i}(1 - p)^{n - 2i}$
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
2722
Exploring $ \sum_{n=0}^\infty \frac{n^p}{n!} = B_pe$, particularly $p = 2$.