User stewbasic - Mathematics Stack Exchange

61 votes

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$...

answered Jul 10, 2017 at 23:31

36 votes

Accepted

Solve 6th degree polynomial: $(x^2 - 3x - 4)(x^2 - 5x + 6)(x^2 + 2x) + 30$

answered Sep 22, 2016 at 0:54

19 votes

Accepted

Solutions to $f'=f$ over the rationals

answered Aug 22, 2016 at 4:57

16 votes

If $(A-B)^2=AB$, prove that $\det(AB-BA)=0$.

answered Apr 19, 2017 at 3:00

14 votes

What is the fewest number of squares required to cover a $11\times13\text{ cm}$ rectangle without overlap?

answered Sep 9, 2016 at 1:43

13 votes

Accepted

Functional Equation $f(x+f(x))=x+f(x)$

answered May 2, 2018 at 2:10

11 votes

Find all functions $f\colon \mathbb{R}^* \to \mathbb{R}^* $ satisfying $f(xyz)=f(xy+yz+xz)\big(f(x)+f(y)+f(z)\big)$ when $xy+yz+xz\ne 0$

answered Jun 23, 2016 at 4:54

10 votes

Accepted

Does this operation exist? What's its name?

answered Oct 10, 2016 at 0:15

7 votes

How to show the Jungle River Metric is Complete

answered Oct 10, 2017 at 0:31

6 votes

Accepted

Does the series $\sum_{n=1}^{\infty}\frac{\sin(\cos(n))}{n}$ converge?

answered Apr 18, 2017 at 3:48

6 votes

Accepted

Hard inequality with cos() and sin()

answered Aug 1, 2017 at 3:21

6 votes

Accepted

how to prove that $I \cong \mathrm{Hom}_R(I,R)$

answered Aug 18, 2016 at 5:36

6 votes

Accepted

Find the function $f(x)$ if $f(x+2f(y))=f(x)+y+f(y)$

answered Sep 23, 2016 at 6:54

6 votes

Accepted

What is the set of triangular numbers mod $n$?

answered Sep 26, 2016 at 22:32

6 votes

Accepted

If GCD $(a_1,\ldots, a_n)=1$ then there's a matrix in $SL_n(\mathbb{Z})$ with first row $(a_1,\ldots, a_n)$

answered Jun 21, 2016 at 2:40

6 votes

Accepted

Is $x^5 + x^3 + 1$ irreducible in $\mathbb{F}_{32}$ and $\mathbb{F}_8$?

answered Jul 11, 2016 at 1:16

5 votes

Accepted

Prove that $\Bbb{R}[\cos(\theta),\sin(\theta)]\cong\Bbb{R}[x,y]/(1-x^2-y^2)$

answered Jun 22, 2016 at 0:46

5 votes

Accepted

Irreducibility of a polynomial with no roots over $K$, $\mbox{char} K= p$

answered Sep 29, 2016 at 6:45

5 votes

Can the boy escape the teacher for a regular $n$-gon?

answered Oct 24, 2017 at 21:22

5 votes

True or false : $\gcd(a_m, a_n) = a_{\gcd(m, n)}$?

answered Sep 26, 2017 at 4:46

5 votes

How does calculus without Euler's number (e) look?

answered Oct 12, 2017 at 3:19

4 votes

Must a multiplicative bijection on a ring $R \rightarrow R'$ with all elements nilpotent or units be an isomorphism?

answered Sep 21, 2017 at 22:06

4 votes

Restricted Nim : Similarities between problem sets

answered Sep 26, 2017 at 4:20

4 votes

Accepted

Stabilizer of a Group Action

answered Aug 21, 2017 at 22:53

4 votes

Accepted

Normal Group and Conjugacy Class

answered Jul 24, 2017 at 23:56

4 votes

How many coefficients do you have to change to lower the rank of a matrix?

answered Jul 28, 2017 at 23:46

4 votes

Accepted

$\frac{xy}{z+1}+\frac{yz}{x+1}+\frac{zx}{y+1}$ is an integer

answered May 9, 2017 at 6:30

4 votes

Accepted

In a coxeter group, if $s_1\dots s_n=t_1\dots t_n$ then $t_1s_1\cdots s_r=s_1\cdots s_{r+1}$?

answered Oct 4, 2016 at 0:03

4 votes

How can I turn $(a_n-a_{n-1})^2-4a_na_{n-1}-8=0$ into $a_n=\frac12\left((1+\sqrt2)^{2n+1}+(1-\sqrt2)^{2n+1}\right)$?

answered Sep 16, 2016 at 5:24

4 votes

Accepted

How did I mix up this expected value problem (Project Euler 151)?

answered Aug 18, 2016 at 4:17

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162 Answers

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$...

Solve 6th degree polynomial: $(x^2 - 3x - 4)(x^2 - 5x + 6)(x^2 + 2x) + 30$

Solutions to $f'=f$ over the rationals

If $(A-B)^2=AB$, prove that $\det(AB-BA)=0$.

What is the fewest number of squares required to cover a $11\times13\text{ cm}$ rectangle without overlap?

Functional Equation $f(x+f(x))=x+f(x)$

Find all functions $f\colon \mathbb{R}^* \to \mathbb{R}^* $ satisfying $f(xyz)=f(xy+yz+xz)\big(f(x)+f(y)+f(z)\big)$ when $xy+yz+xz\ne 0$

Does this operation exist? What's its name?

How to show the Jungle River Metric is Complete

Does the series $\sum_{n=1}^{\infty}\frac{\sin(\cos(n))}{n}$ converge?

Hard inequality with cos() and sin()

how to prove that $I \cong \mathrm{Hom}_R(I,R)$

Find the function $f(x)$ if $f(x+2f(y))=f(x)+y+f(y)$

What is the set of triangular numbers mod $n$?

If GCD $(a_1,\ldots, a_n)=1$ then there's a matrix in $SL_n(\mathbb{Z})$ with first row $(a_1,\ldots, a_n)$

Is $x^5 + x^3 + 1$ irreducible in $\mathbb{F}_{32}$ and $\mathbb{F}_8$?

Prove that $\Bbb{R}[\cos(\theta),\sin(\theta)]\cong\Bbb{R}[x,y]/(1-x^2-y^2)$

Irreducibility of a polynomial with no roots over $K$, $\mbox{char} K= p$

Can the boy escape the teacher for a regular $n$-gon?

True or false : $\gcd(a_m, a_n) = a_{\gcd(m, n)}$?

How does calculus without Euler's number (e) look?

Must a multiplicative bijection on a ring $R \rightarrow R'$ with all elements nilpotent or units be an isomorphism?

Restricted Nim : Similarities between problem sets

Stabilizer of a Group Action

Normal Group and Conjugacy Class

How many coefficients do you have to change to lower the rank of a matrix?

$\frac{xy}{z+1}+\frac{yz}{x+1}+\frac{zx}{y+1}$ is an integer

In a coxeter group, if $s_1\dots s_n=t_1\dots t_n$ then $t_1s_1\cdots s_r=s_1\cdots s_{r+1}$?

How can I turn $(a_n-a_{n-1})^2-4a_na_{n-1}-8=0$ into $a_n=\frac12\left((1+\sqrt2)^{2n+1}+(1-\sqrt2)^{2n+1}\right)$?

How did I mix up this expected value problem (Project Euler 151)?