User math110

6 votes

0 answers

473 views

For which rational values of $c$ and $d$ are the numbers $\sin{(\pi\cdot c)}$, $\sin{(\pi\cdot d)}$ and $1$ linearly dependent over $\mathbb{Q}$?

asked Jan 15, 2015 at 4:19

6 votes

1 answer

943 views

Irreducible polynomial $p_{n}(x)=\sum_{k=0}^{n}\frac{x^k}{k!}$ for all positive integers $n$

asked May 30, 2016 at 6:28

5 votes

1 answer

643 views

Do there exist infinitely many $n$ such that $n^3+an+b$ is squarefree?

asked Apr 5, 2016 at 4:49

5 votes

0 answers

2k views

A stronger Cauchy-Schwarz inequality for traces of compression matrices

asked Jun 19, 2014 at 14:44

5 votes

3 answers

571 views

Find the best constant to this bounded inequality

asked Jul 9, 2016 at 15:21

5 votes

1 answer

330 views

maybe this conjecture also hold to this complex inequality

asked Jul 14, 2016 at 14:24

5 votes

1 answer

395 views

Prove this conjecture inequality $x\cdot \frac{(1-x)^{k-1}}{(k+1)^{k-2}}+\frac{(1-2x)^k}{k^k}\le \frac{1}{(k+2)^{k-1}}$

asked Oct 25, 2017 at 8:46

5 votes

2 answers

921 views

On the upper bound of $\sum_{i=1}^{n}x^m_{i}$ subject to the conditions $\sum_{i=1}^{n}x_{i}=0$ and $\sum_{i=1}^{n}x^2_{i}=n$

asked Sep 15, 2018 at 11:52

5 votes

1 answer

339 views

A variant of Cauchy-type functional equation conjecture

asked Oct 13, 2018 at 11:56

5 votes

2 answers

925 views

How to show this symmetric function inequality

asked Feb 6, 2021 at 15:59

5 votes

3 answers

269 views

Find the maximum trigonometric polynomial coefficient $A_{k}$

asked Jan 27, 2021 at 4:38

4 votes

1 answer

676 views

How to solve this equation $a^2+3b^2c^2=7^c$

asked Nov 17, 2020 at 3:54

4 votes

1 answer

579 views

Find all rational solutions of $x^2(x+1)(x^2+1)(x-1)=2(y+1)(y-1)$

asked Dec 1, 2016 at 9:28

4 votes

0 answers

317 views

there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

asked Dec 27, 2016 at 6:55

4 votes

0 answers

251 views

How find this binomial-coefficients sum $\sum_{k_{1}+k_{2}+\cdots+k_{d}=n}\binom{n}{k_{1},k_{2},\cdots,k_{d}}^2$ [duplicate]

asked Oct 27, 2014 at 16:56

4 votes

1 answer

330 views

maybe Faulhaber polynomial $S_{k}(x)=0$ have only rational roots $0,-\frac{1}{2},-1$

asked Apr 13, 2023 at 1:02

3 votes

1 answer

735 views

A similar Cauchy-Schwarz inequality with linear-algebra

asked Jun 18, 2014 at 22:52

3 votes

1 answer

569 views

Prove this conjecture inequality

asked May 12, 2016 at 4:20

3 votes

1 answer

842 views

Find all positive integers $n$ such that $n+\tau{(n)}=2\varphi{(n)}$

asked Mar 20, 2018 at 14:50

3 votes

1 answer

355 views

Solve this diophantine equation: $m^4+n^4=10m^2n^2+1$

asked May 26, 2017 at 4:39

3 votes

1 answer

467 views

How to prove this combinatorial identity?

asked May 26, 2020 at 7:22

3 votes

0 answers

320 views

is $\sum_{i=1}^{n}\sum_{j=1}^{n}|a_{i}+a_{j}|\cdot p_{i}p_{j}\ge \sum_{i=1}^{n}p_{i}|a_{i}|$?

asked Feb 6, 2021 at 0:45

3 votes

1 answer

908 views

Prove that $\frac{2^n-2}{n}$ is composite number

asked Sep 15, 2021 at 7:52

3 votes

1 answer

205 views

it's convex sequence inequality

asked Oct 12, 2018 at 4:11

2 votes

1 answer

305 views

Logarithmic and polynomial functions with two roots

asked Feb 7, 2019 at 14:26

2 votes

3 answers

425 views

Find a distinct postive integer solution to this $xyzw=504(x^2+y^2+z^2+w^2)$ diophantine equation

asked Jul 17, 2016 at 6:55

2 votes

0 answers

274 views

For which constant $d$ this polynomial is reducible over $\mathbb Q$? [closed]

asked Jan 6, 2014 at 2:44

2 votes

0 answers

246 views

A integral equation with Discrete to result by inverse problem

asked Jan 5, 2015 at 16:01

2 votes

1 answer

333 views

Determine whether a system of polynomials with real coefficients has a real solution?

asked Jan 16, 2015 at 13:29

2 votes

2 answers

2k views

Find all rational solutions of this diophantine-equation?

asked Jun 7, 2015 at 14:34

Stack Exchange Network

75 Questions

For which rational values of $c$ and $d$ are the numbers $\sin{(\pi\cdot c)}$, $\sin{(\pi\cdot d)}$ and $1$ linearly dependent over $\mathbb{Q}$?

Irreducible polynomial $p_{n}(x)=\sum_{k=0}^{n}\frac{x^k}{k!}$ for all positive integers $n$

Do there exist infinitely many $n$ such that $n^3+an+b$ is squarefree?

A stronger Cauchy-Schwarz inequality for traces of compression matrices

Find the best constant to this bounded inequality

maybe this conjecture also hold to this complex inequality

Prove this conjecture inequality $x\cdot \frac{(1-x)^{k-1}}{(k+1)^{k-2}}+\frac{(1-2x)^k}{k^k}\le \frac{1}{(k+2)^{k-1}}$

On the upper bound of $\sum_{i=1}^{n}x^m_{i}$ subject to the conditions $\sum_{i=1}^{n}x_{i}=0$ and $\sum_{i=1}^{n}x^2_{i}=n$

A variant of Cauchy-type functional equation conjecture

How to show this symmetric function inequality

Find the maximum trigonometric polynomial coefficient $A_{k}$

How to solve this equation $a^2+3b^2c^2=7^c$

Find all rational solutions of $x^2(x+1)(x^2+1)(x-1)=2(y+1)(y-1)$

there exist infinite many $n\in\mathbb{N}$ such that $S_n-[S_n]<\frac{1}{n^2}$

How find this binomial-coefficients sum $\sum_{k_{1}+k_{2}+\cdots+k_{d}=n}\binom{n}{k_{1},k_{2},\cdots,k_{d}}^2$ [duplicate]

maybe Faulhaber polynomial $S_{k}(x)=0$ have only rational roots $0,-\frac{1}{2},-1$

A similar Cauchy-Schwarz inequality with linear-algebra

Prove this conjecture inequality

Find all positive integers $n$ such that $n+\tau{(n)}=2\varphi{(n)}$

Solve this diophantine equation: $m^4+n^4=10m^2n^2+1$

How to prove this combinatorial identity?

is $\sum_{i=1}^{n}\sum_{j=1}^{n}|a_{i}+a_{j}|\cdot p_{i}p_{j}\ge \sum_{i=1}^{n}p_{i}|a_{i}|$?

Prove that $\frac{2^n-2}{n}$ is composite number

it's convex sequence inequality

Logarithmic and polynomial functions with two roots

Find a distinct postive integer solution to this $xyzw=504(x^2+y^2+z^2+w^2)$ diophantine equation

For which constant $d$ this polynomial is reducible over $\mathbb Q$? [closed]

A integral equation with Discrete to result by inverse problem

Determine whether a system of polynomials with real coefficients has a real solution?

Find all rational solutions of this diophantine-equation?