User math110

38 votes

4 answers

4k views

A family of polynomials whose zeros all lie on the unit circle

asked May 3, 2018 at 9:20

12 votes

3 answers

3k views

How do we show this matrix has full rank?

asked Dec 30, 2014 at 16:00

24 votes

4 answers

2k views

This inequality why can't solve it by now (Only four variables inequality)?

asked Jan 12, 2015 at 17:02

16 votes

4 answers

2k views

An inequality concerning Lagrange's identity

asked May 19, 2016 at 2:40

43 votes

3 answers

2k views

Proving $\sum_{i=1}^{n}\sum_{j=1}^{n}\left\{\frac{x_{i}}{x_{j}}\right\}\le \frac{9}{14}n^2$？

asked Jan 3 at 15:25

20 votes

4 answers

2k views

When is $1^n+2^n+3^n+4^n+\cdots+n^n$ a square number?

asked Mar 5, 2018 at 13:28

5 votes

0 answers

2k views

A stronger Cauchy-Schwarz inequality for traces of compression matrices

asked Jun 19, 2014 at 14:44

13 votes

3 answers

2k views

I conjecture inequalities $\sum_{k=1}^{n}\{kx\}\le\frac{n}{2}x$

asked Nov 10, 2018 at 1:20

2 votes

2 answers

2k views

Find all rational solutions of this diophantine-equation?

asked Jun 7, 2015 at 14:34

14 votes

4 answers

1k views

Find all solution $a,b,c$ with $(1-a^2)(1-b^2)(1-c^2)=8abc$

asked Jun 5, 2015 at 1:17

16 votes

1 answer

1k views

Solve this Diophantine equation $(2^x-1)(3^y-1)=2z^2$

asked Apr 1, 2018 at 4:47

24 votes

4 answers

1k views

show this nice and hard inequality with $ \prod_{i=1}^{n}|x_{i}-y_{i}|<e^{\frac{n}{2}}$

asked Oct 11, 2018 at 8:29

24 votes

2 answers

1k views

Is $\iiint_{[0, 1]^3} \lvert f(x)+f(y)+f(z)\rvert\, dx\, dy\, dz \ge \int_0^1 \lvert f(x)\rvert\, dx$?

asked Feb 5, 2021 at 6:28

9 votes

2 answers

1k views

How to prove this inequality of Karamata type?

asked May 29, 2019 at 0:50

6 votes

1 answer

918 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

2 answers

916 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

2 answers

914 views

How to show this symmetric function inequality

asked Feb 6, 2021 at 15:59

7 votes

3 answers

899 views

Prove $ n!$ is divisible by the number of its positive divisors

asked May 24, 2018 at 1:22

3 votes

1 answer

869 views

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

asked Sep 15, 2021 at 7:52

6 votes

3 answers

785 views

Is there a simple proof that $Ax^3+By^3=C$ has only finitely many integer solutions

asked Feb 6, 2021 at 1:25

7 votes

2 answers

736 views

Conjecture: $a^n+b^n+c^n\ge x^n+y^n+z^n$

asked Apr 3, 2019 at 3:50

10 votes

2 answers

733 views

Find all $m$ such $2^m+1\mid5^m-1$

asked Dec 14, 2018 at 1:34

3 votes

1 answer

732 views

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

asked Mar 20, 2018 at 14:50

6 votes

1 answer

709 views

Find the maximum of $|a_{p}|$, if $a_0+a_1x+\dots+a_nx^n:[-1,1]\mapsto [-1,1]$

asked Dec 23, 2016 at 12:11

3 votes

1 answer

708 views

A similar Cauchy-Schwarz inequality with linear-algebra

asked Jun 18, 2014 at 22:52

8 votes

1 answer

668 views

Prove an inequality related to sums of Legendre symbols

asked Apr 12, 2022 at 0:34

13 votes

2 answers

665 views

Show that there exist $k\in\{1,2,\cdots,n\}$ such that $\frac{1}{n}\sum_{i=1}^{n}\left(\{kx_{i}\}-\frac{1}{2}\right)^2>\frac{1}{12}-\frac{1}{6n}$

asked Sep 13, 2018 at 7:46

8 votes

0 answers

664 views

How prove this polynomial inequality from a book

asked Dec 12, 2014 at 12:22

6 votes

0 answers

662 views

Show this number always is composite number

asked May 8, 2018 at 11:15

4 votes

1 answer

648 views

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

asked Nov 17, 2020 at 3:54

Stack Exchange Network

75 Questions

A family of polynomials whose zeros all lie on the unit circle

How do we show this matrix has full rank?

This inequality why can't solve it by now (Only four variables inequality)?

An inequality concerning Lagrange's identity

Proving $\sum_{i=1}^{n}\sum_{j=1}^{n}\left\{\frac{x_{i}}{x_{j}}\right\}\le \frac{9}{14}n^2$？

When is $1^n+2^n+3^n+4^n+\cdots+n^n$ a square number?

A stronger Cauchy-Schwarz inequality for traces of compression matrices

I conjecture inequalities $\sum_{k=1}^{n}\{kx\}\le\frac{n}{2}x$

Find all rational solutions of this diophantine-equation?

Find all solution $a,b,c$ with $(1-a^2)(1-b^2)(1-c^2)=8abc$

Solve this Diophantine equation $(2^x-1)(3^y-1)=2z^2$

show this nice and hard inequality with $ \prod_{i=1}^{n}|x_{i}-y_{i}|<e^{\frac{n}{2}}$

Is $\iiint_{[0, 1]^3} \lvert f(x)+f(y)+f(z)\rvert\, dx\, dy\, dz \ge \int_0^1 \lvert f(x)\rvert\, dx$?

How to prove this inequality of Karamata type?

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

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

How to show this symmetric function inequality

Prove $ n!$ is divisible by the number of its positive divisors

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

Is there a simple proof that $Ax^3+By^3=C$ has only finitely many integer solutions

Conjecture: $a^n+b^n+c^n\ge x^n+y^n+z^n$

Find all $m$ such $2^m+1\mid5^m-1$

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

Find the maximum of $|a_{p}|$, if $a_0+a_1x+\dots+a_nx^n:[-1,1]\mapsto [-1,1]$

A similar Cauchy-Schwarz inequality with linear-algebra

Prove an inequality related to sums of Legendre symbols

Show that there exist $k\in\{1,2,\cdots,n\}$ such that $\frac{1}{n}\sum_{i=1}^{n}\left(\{kx_{i}\}-\frac{1}{2}\right)^2>\frac{1}{12}-\frac{1}{6n}$

How prove this polynomial inequality from a book

Show this number always is composite number

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