User Clyde Kertzer

14 votes

2 answers

847 views

Peculiar pattern in the Collatz sequence

asked Oct 11, 2022 at 1:07

5 votes

3 answers

171 views

Classify, up to similarity, the $3$ by $3$ matrices with coefficients in $\mathbb{Q}$ that satisfy $A^6=I$.

asked May 7 at 4:34

4 votes

3 answers

493 views

Denominators of fractions are closed under gcd (vector gcds)

asked Apr 6, 2022 at 16:39

4 votes

2 answers

601 views

Does a generalized difference of powers formula exist?

asked Apr 7, 2022 at 17:15

3 votes

1 answer

467 views

Is there a way to find the $n$th term of a Farey sequence?

asked Mar 30, 2022 at 23:29

3 votes

4 answers

692 views

Does there exist such a Riemann integrable function?

asked Apr 15, 2022 at 20:43

3 votes

1 answer

104 views

Show that $\lim _{n \rightarrow \infty} \frac{1}{4^n} h\left(2^n P\right)$ exists

asked Mar 3, 2023 at 0:14

2 votes

2 answers

132 views

In $\triangle ABC$, $DE$ parallel to $BC$, $F$ midpoint of $DE$, $AF$ meets $BC$ at $G$. Prove $G$ is the midpoint of $BC$

asked Feb 17, 2023 at 1:17

2 votes

1 answer

194 views

Solutions to the Diophantine equation $(ab)(a+b) = N$

asked Apr 12, 2023 at 18:48

2 votes

6 answers

243 views

Show that $\int_{-\infty}^{\infty} \frac{x^2}{\left(x^2+a^2\right)^2} dx = \frac{\pi}{2a}$

asked Apr 11 at 23:08

2 votes

1 answer

119 views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

asked Oct 20, 2023 at 16:51

2 votes

1 answer

97 views

Show that $n$ has $2^{\omega(n) - 1}$ coprime factor pairs

asked Nov 27, 2023 at 19:54

2 votes

2 answers

214 views

Conjecture: Every $n \geq 20 \in \mathbb{N}$ can be written as a sum of three integers $(\geq 2)$ that are pairwise coprime

asked Apr 24, 2022 at 0:10

2 votes

2 answers

654 views

Use the definition of the derivative to differentiate $e^{-1/x^2}$

asked Mar 28, 2022 at 23:43

1 vote

1 answer

334 views

Has the sum of 4 cubes problem been proven?

asked Apr 5, 2022 at 2:43

1 vote

3 answers

294 views

Show that $f$ is Riemann integrable and that $\int_a^b f (x)dx = 0$

asked Apr 12, 2022 at 18:52

1 vote

2 answers

532 views

How to prove a limit of a function does not exist?

asked Feb 28, 2022 at 19:32

1 vote

1 answer

96 views

Find integer solutions to$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=3$ [duplicate]

asked Apr 27, 2022 at 15:52

1 vote

3 answers

241 views

Show $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots+\frac{1}{1999}-\frac{1}{2000} =\frac{1}{1001}+\frac{1}{1002}+\ldots+\frac{1}{1999}+\frac{1}{2000}$

asked Apr 16, 2022 at 23:15

1 vote

1 answer

155 views

Show that $\sum_{k=1}^nk {n \choose 2k+1}=(n-2)2^{n-3}$

asked Apr 19, 2022 at 18:03

1 vote

2 answers

265 views

Is $f(x)=(\sin (1/x))^4$ Riemann integrable on $(0,1]$?

asked Apr 20, 2022 at 4:08

1 vote

1 answer

350 views

Power series expansion of $\arctan (x)$ centered at $x=0$ extends to $x=1$?

asked Oct 18, 2022 at 2:55

1 vote

2 answers

169 views

Prove $f(r, \theta) = (\cos\theta, \sin\theta)$ is continuous

asked Nov 8, 2022 at 1:25

1 vote

1 answer

800 views

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

asked Dec 12, 2022 at 23:02

1 vote

1 answer

367 views

Is $C([0,1])$ complete if $\int_{0}^{1} f(x)g(x)dx$ is the inner product?

asked Dec 6, 2022 at 0:27

1 vote

1 answer

114 views

Find intersection points of $x^2 - 3xy+ 2y^2 - x + 1 = 0$ and $y = \alpha x + \beta$

asked Feb 6, 2023 at 17:16

1 vote

2 answers

237 views

Find rational solutions to $x^2 + y^2 = 6$

asked Feb 9, 2023 at 0:04

1 vote

1 answer

71 views

Show that the point $[0,1,0]$ is a non-singular point of $C$

asked Feb 14, 2023 at 6:54

1 vote

1 answer

298 views

What is the difference between an $FG$-module and a group algebra?

asked Feb 15, 2023 at 1:08

1 vote

2 answers

119 views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

asked Oct 20, 2023 at 19:16

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60 Questions

Peculiar pattern in the Collatz sequence

Classify, up to similarity, the $3$ by $3$ matrices with coefficients in $\mathbb{Q}$ that satisfy $A^6=I$.

Denominators of fractions are closed under gcd (vector gcds)

Does a generalized difference of powers formula exist?

Is there a way to find the $n$th term of a Farey sequence?

Does there exist such a Riemann integrable function?

Show that $\lim _{n \rightarrow \infty} \frac{1}{4^n} h\left(2^n P\right)$ exists

In $\triangle ABC$, $DE$ parallel to $BC$, $F$ midpoint of $DE$, $AF$ meets $BC$ at $G$. Prove $G$ is the midpoint of $BC$

Solutions to the Diophantine equation $(ab)(a+b) = N$

Show that $\int_{-\infty}^{\infty} \frac{x^2}{\left(x^2+a^2\right)^2} dx = \frac{\pi}{2a}$

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

Show that $n$ has $2^{\omega(n) - 1}$ coprime factor pairs

Conjecture: Every $n \geq 20 \in \mathbb{N}$ can be written as a sum of three integers $(\geq 2)$ that are pairwise coprime

Use the definition of the derivative to differentiate $e^{-1/x^2}$

Has the sum of 4 cubes problem been proven?

Show that $f$ is Riemann integrable and that $\int_a^b f (x)dx = 0$

How to prove a limit of a function does not exist?

Find integer solutions to$\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=3$ [duplicate]

Show $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\ldots+\frac{1}{1999}-\frac{1}{2000} =\frac{1}{1001}+\frac{1}{1002}+\ldots+\frac{1}{1999}+\frac{1}{2000}$

Show that $\sum_{k=1}^nk {n \choose 2k+1}=(n-2)2^{n-3}$

Is $f(x)=(\sin (1/x))^4$ Riemann integrable on $(0,1]$?

Power series expansion of $\arctan (x)$ centered at $x=0$ extends to $x=1$?

Prove $f(r, \theta) = (\cos\theta, \sin\theta)$ is continuous

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

Is $C([0,1])$ complete if $\int_{0}^{1} f(x)g(x)dx$ is the inner product?

Find intersection points of $x^2 - 3xy+ 2y^2 - x + 1 = 0$ and $y = \alpha x + \beta$

Find rational solutions to $x^2 + y^2 = 6$

Show that the point $[0,1,0]$ is a non-singular point of $C$

What is the difference between an $FG$-module and a group algebra?

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$