User Rijul Saini

29 votes

Accepted

Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.

answered Aug 28, 2012 at 19:33

26 votes

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Mysterious sum equal to $\frac{7(p^2-1)}{24}$ where $p \equiv 1 \pmod{4}$

answered Feb 16 at 20:07

11 votes

Accepted

How to evaluate $\int \frac{\mathrm dx}{\sqrt[3]{\tan\,x}}$?

answered Jul 31, 2012 at 11:13

10 votes

Inequality. $ab^2+bc^2+ca^2 \geq a+b+c.$

answered Sep 5, 2012 at 14:30

7 votes

Accepted

Friendly graph partitioning

answered Oct 6, 2014 at 5:08

6 votes

Accepted

Inequality. $\sqrt{\frac{ab+bc+ca}{3}} \leq \sqrt[3]{\frac{(a+b)(b+c)(c+a)}{8}}$

answered Sep 12, 2012 at 9:26

6 votes

Accepted

Solve over natural numbers: $m^3=2n^3+6n^2$. Functional equation gives rise to a diophantine equation!

answered Feb 18 at 21:46

6 votes

Evaluate $\int\frac{dx}{\sin(x+a)\sin(x+b)}$

answered Sep 4, 2012 at 20:10

6 votes

Calculating the residue of power towers

answered Aug 18, 2012 at 8:01

6 votes

Prove that: $\sin(x) \cos(x) \geq x-x^3$

answered Aug 23, 2012 at 9:16

5 votes

Accepted

Prove $\frac{1}{a(1+b)} + \frac{1}{b(1+c)} + \frac{1}{c(1+a)} \geq \frac{3}{ (abc)^{\frac{1}{3}}\big( 1+ (abc)^{\frac{1}{3}}\big) }$ using AM-GM

answered Sep 15, 2012 at 15:23

4 votes

Accepted

Divisors count of $3^n\pm1$

answered Feb 18 at 8:27

4 votes

Dimensions of symmetric and skew-symmetric matrices

answered Aug 23, 2012 at 9:59

4 votes

Accepted

Inequality. $(n+1)\left(a^{n+1}+b^{n+1}\right) \geq (a+b)\left(a^n+a^{n-1}b+\ldots+b^{n}\right). $

answered Sep 9, 2012 at 21:53

3 votes

Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$

answered Sep 9, 2012 at 0:26

3 votes

Ways to Choose Three Adjacent Elements from a Set

answered Sep 4, 2012 at 21:07

3 votes

Integral inequality on a periodic function

answered Sep 4, 2012 at 13:19

3 votes

Showing that $ \left( \frac{a+2b}{a+2c}\right)^3+\left( \frac{b+2c}{b+2a}\right)^3+\left( \frac{c+2a}{c+2b}\right)^3 \geq3 $

answered Aug 29, 2012 at 20:37

3 votes

Prove $x^{4}+y^{4}+z^{4}\geq x^{2}yz+xy^{2}z+xyz^{2}$ trivially?

answered Sep 4, 2012 at 20:07

3 votes

Convergence\Divergence of $\sum\limits_{n=1}^{\infty}\frac {1\cdot 3\cdots (2n-1)} {2\cdot 4\cdots (2n)}$

answered Aug 18, 2012 at 8:10

3 votes

Accepted

How to show $A$ cannot have more than one Jordan block for any eigenvalue?

answered Jul 31, 2012 at 12:48

3 votes

Prove $\sin^2(A)+\sin^2(B)-\sin^2(C)=2\sin(A)\sin(B) \cos(C)$ if $A+B+C=180$ degrees

answered Jul 31, 2012 at 15:29

3 votes

To show the set is dense in $\mathbb{R}$

answered Jul 31, 2012 at 16:10

3 votes

Accepted

modified $\sum{k{n \choose k}}$ closed form expression

answered Jul 31, 2012 at 19:43

3 votes

A binomial identity

answered Aug 9, 2012 at 21:35

2 votes

Accepted

$2$ question on matrix with some condition

answered Aug 14, 2012 at 20:48

2 votes

Maximum area of a triangle

answered Jul 31, 2012 at 15:41

2 votes

Accepted

Limit of a sequence of matrices

answered Aug 20, 2012 at 9:49

2 votes

In a polynomial of $n$ degree, what numbers can fill the $n$?

answered Aug 23, 2012 at 10:30

2 votes

Accepted

Minimize the sum of tangents when sum of angles are constants

answered Aug 28, 2012 at 19:48

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44 Answers

Showing that the roots of a polynomial with descending positive coefficients lie in the unit disc.

Mysterious sum equal to $\frac{7(p^2-1)}{24}$ where $p \equiv 1 \pmod{4}$

How to evaluate $\int \frac{\mathrm dx}{\sqrt[3]{\tan\,x}}$?

Inequality. $ab^2+bc^2+ca^2 \geq a+b+c.$

Friendly graph partitioning

Inequality. $\sqrt{\frac{ab+bc+ca}{3}} \leq \sqrt[3]{\frac{(a+b)(b+c)(c+a)}{8}}$

Solve over natural numbers: $m^3=2n^3+6n^2$. Functional equation gives rise to a diophantine equation!

Evaluate $\int\frac{dx}{\sin(x+a)\sin(x+b)}$

Calculating the residue of power towers

Prove that: $\sin(x) \cos(x) \geq x-x^3$

Prove $\frac{1}{a(1+b)} + \frac{1}{b(1+c)} + \frac{1}{c(1+a)} \geq \frac{3}{ (abc)^{\frac{1}{3}}\big( 1+ (abc)^{\frac{1}{3}}\big) }$ using AM-GM

Divisors count of $3^n\pm1$

Dimensions of symmetric and skew-symmetric matrices

Inequality. $(n+1)\left(a^{n+1}+b^{n+1}\right) \geq (a+b)\left(a^n+a^{n-1}b+\ldots+b^{n}\right). $

Inequality.$\sqrt{\frac{2a}{b+c}}+\sqrt{\frac{2b}{c+a}}+\sqrt{\frac{2c}{a+b}} \leq 3$

Ways to Choose Three Adjacent Elements from a Set

Integral inequality on a periodic function

Showing that $ \left( \frac{a+2b}{a+2c}\right)^3+\left( \frac{b+2c}{b+2a}\right)^3+\left( \frac{c+2a}{c+2b}\right)^3 \geq3 $

Prove $x^{4}+y^{4}+z^{4}\geq x^{2}yz+xy^{2}z+xyz^{2}$ trivially?

Convergence\Divergence of $\sum\limits_{n=1}^{\infty}\frac {1\cdot 3\cdots (2n-1)} {2\cdot 4\cdots (2n)}$

How to show $A$ cannot have more than one Jordan block for any eigenvalue?

Prove $\sin^2(A)+\sin^2(B)-\sin^2(C)=2\sin(A)\sin(B) \cos(C)$ if $A+B+C=180$ degrees

To show the set is dense in $\mathbb{R}$

modified $\sum{k{n \choose k}}$ closed form expression

A binomial identity

$2$ question on matrix with some condition

Maximum area of a triangle

Limit of a sequence of matrices

In a polynomial of $n$ degree, what numbers can fill the $n$?

Minimize the sum of tangents when sum of angles are constants