User Donald Splutterwit

5 votes

The identity $\arctan(x) + \arctan(x^3) = \arctan(2x+\sqrt{3}) + \arctan(2x-\sqrt{3})$

answered Sep 28, 2020 at 13:32

5 votes

Accepted

If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$

answered Aug 27, 2020 at 22:29

5 votes

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

answered May 17, 2020 at 19:12

5 votes

Given that $a+b+c=0$, show that $2(a^4+b^4+c^4)$ is a perfect square

answered Mar 31, 2020 at 3:10

5 votes

Japanese Temple Geometry Problem: Two tangent lines and three tangent circles.

answered Feb 24, 2020 at 4:58

5 votes

Accepted

Changing index in summation

answered Feb 14, 2020 at 3:00

4 votes

Is the complement of a C7 graph planar or non-planar?

answered Mar 1, 2018 at 19:55

4 votes

Accepted

Calculating an expression using recursive formulas

answered Dec 31, 2017 at 18:36

4 votes

Pigeonhole principle with cartesian product

answered Dec 23, 2017 at 14:05

4 votes

How can i calculate the height of number in this triangular?

answered Dec 20, 2017 at 11:56

4 votes

Accepted

Find inverse of a matrix filled with 1 and -1 on main diagonal

answered Dec 1, 2017 at 20:04

4 votes

Accepted

$A^{-1}=\alpha A+\beta I$

answered Nov 24, 2017 at 22:00

4 votes

How can i prove that $AB=BA$?

answered Nov 27, 2017 at 20:32

4 votes

Show that $\Bbb Z\Big(\frac{1+\sqrt{d}}{2}\Big)$ is closed under multiplication.

answered Jan 22, 2018 at 20:42

4 votes

Determine x and y for polar graphs with the angle (2 $\theta$)

answered May 29, 2017 at 9:33

4 votes

Accepted

Minimum degree rational equation with root $a+\sqrt{b}+\sqrt{c}+\sqrt{d}$.

answered Apr 14, 2017 at 21:00

4 votes

Accepted

If $a,b,c\in N$, such that $aaaaaa=bcbc(b+b+c)(c+c-b)(c-b)$, then find $a,b,c$.

answered Apr 23, 2017 at 13:41

4 votes

Accepted

Find the sum of this series of coefficients of $(1+x+x^2)^n$.

answered Feb 20, 2017 at 17:01

4 votes

How many barcodes are there?

answered Mar 11, 2017 at 13:31

4 votes

Accepted

Evaluate an infinite convergent sum

answered Mar 12, 2017 at 20:35

4 votes

Prove that $\sum\limits_{cyc}\frac{a^2-bd}{b+2c+d}\geq0$

answered Apr 3, 2017 at 15:41

4 votes

Accepted

Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$

answered Feb 9, 2017 at 0:32

4 votes

Find the maximum positive integer that divides $n^7+n^6-n^5-n^4$

answered Jul 30, 2017 at 23:59

4 votes

Showing that $S=\frac{1}{100} + \frac{1}{101} + \dots + \frac{1}{1000} \gt 1$

answered Aug 3, 2017 at 19:58

4 votes

Simplify $x^{\frac{2}{3}}+3x^{\frac{1}{3}}-2=0$ to $x^2 +45x-8=0$

answered Jul 1, 2017 at 8:49

4 votes

Why does $a^2x^2+(a^2+b^2-c^2)xy+b^2y^2>0,$ imply $(a^2+b^2-c^2)^2-4a^2b^2<0$?

answered Jul 19, 2017 at 22:48

4 votes

Accepted

Calculate the sum of the series $\sum_{1\leq a<b<c \\a,b,c\in \mathbb{N}} \frac{1}{2^a 3^b 5^c}$

answered Jun 18, 2017 at 22:00

4 votes

Catalan number sequence problem

answered Oct 31, 2017 at 22:13

4 votes

Accepted

How can I show that $AΔB = A^c Δ B^c$?

answered Oct 8, 2017 at 20:31

4 votes

Accepted

summation of product

answered Oct 10, 2017 at 20:21

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1,386 Answers

The identity $\arctan(x) + \arctan(x^3) = \arctan(2x+\sqrt{3}) + \arctan(2x-\sqrt{3})$

If $a$, $b$, $c$ are the roots of $x^3-6x^2+3x+1=0$, find all possible values of $a^2b+b^2c+c^2a$

show this sum $\sum_{i=0}^{n}(-1)^{i-j}\binom{n+i}{i}\binom{n+k-i}{k-i}\binom{2n}{n+j-i}=\binom{2n}{n}$

Given that $a+b+c=0$, show that $2(a^4+b^4+c^4)$ is a perfect square

Japanese Temple Geometry Problem: Two tangent lines and three tangent circles.

Changing index in summation

Is the complement of a C7 graph planar or non-planar?

Calculating an expression using recursive formulas

Pigeonhole principle with cartesian product

How can i calculate the height of number in this triangular?

Find inverse of a matrix filled with 1 and -1 on main diagonal

$A^{-1}=\alpha A+\beta I$

How can i prove that $AB=BA$?

Show that $\Bbb Z\Big(\frac{1+\sqrt{d}}{2}\Big)$ is closed under multiplication.

Determine x and y for polar graphs with the angle (2 $\theta$)

Minimum degree rational equation with root $a+\sqrt{b}+\sqrt{c}+\sqrt{d}$.

If $a,b,c\in N$, such that $aaaaaa=bcbc(b+b+c)(c+c-b)(c-b)$, then find $a,b,c$.

Find the sum of this series of coefficients of $(1+x+x^2)^n$.

How many barcodes are there?

Evaluate an infinite convergent sum

Prove that $\sum\limits_{cyc}\frac{a^2-bd}{b+2c+d}\geq0$

Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$

Find the maximum positive integer that divides $n^7+n^6-n^5-n^4$

Showing that $S=\frac{1}{100} + \frac{1}{101} + \dots + \frac{1}{1000} \gt 1$

Simplify $x^{\frac{2}{3}}+3x^{\frac{1}{3}}-2=0$ to $x^2 +45x-8=0$

Why does $a^2x^2+(a^2+b^2-c^2)xy+b^2y^2>0,$ imply $(a^2+b^2-c^2)^2-4a^2b^2<0$?

Calculate the sum of the series $\sum_{1\leq a<b<c \\a,b,c\in \mathbb{N}} \frac{1}{2^a 3^b 5^c}$

Catalan number sequence problem

How can I show that $AΔB = A^c Δ B^c$?

summation of product