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Clyde Kertzer's user avatar
Clyde Kertzer's user avatar
Clyde Kertzer's user avatar
Clyde Kertzer
  • Member for 2 years, 5 months
  • Last seen this week
14 votes
2 answers
824 views

Peculiar pattern in the Collatz sequence

5 votes
3 answers
151 views

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

4 votes
3 answers
490 views

Denominators of fractions are closed under gcd (vector gcds)

4 votes
2 answers
575 views

Does a generalized difference of powers formula exist?

3 votes
1 answer
448 views

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

3 votes
4 answers
686 views

Does there exist such a Riemann integrable function?

3 votes
1 answer
104 views

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

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 $BC$

2 votes
1 answer
193 views

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

2 votes
6 answers
229 views

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

2 votes
1 answer
116 views

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

2 votes
1 answer
97 views

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

2 votes
2 answers
212 views

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

2 votes
2 answers
632 views

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

1 vote
1 answer
306 views

Has the sum of 4 cubes problem been proven?

1 vote
3 answers
290 views

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

1 vote
2 answers
507 views

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

1 vote
1 answer
96 views

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

1 vote
3 answers
236 views

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

1 vote
1 answer
144 views

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

1 vote
2 answers
256 views

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

1 vote
1 answer
342 views

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

1 vote
2 answers
169 views

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

1 vote
1 answer
766 views

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

1 vote
1 answer
347 views

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

1 vote
1 answer
114 views

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

1 vote
2 answers
228 views

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

1 vote
1 answer
69 views

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

1 vote
1 answer
271 views

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

1 vote
2 answers
104 views

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