Connor Harris
  • Member for 8 years, 3 months
  • Last seen more than a month ago
2 answers
48 votes
1k views
19 bookmarks
'flimsy' spaces: removing any $n$ points results in disconnectedness
1 answers
43 votes
602 views
12 bookmarks
What is $\tau(A_n)$?
3 answers
38 votes
1k views
12 bookmarks
What is the period of Langton's ant on a torus?
6 answers
36 votes
1k views
21 bookmarks
New bound for Am-Gm of 2 variables
2 answers
32 votes
1k views
13 bookmarks
The "natural" Sophomore's Dream integral: $\int_{0}^{\infty} x^{-x}\ dx$
2 answers
31 votes
1k views
20 bookmarks
Prove or disprove that, for any $n \in \mathbb{N_+}$, there exist $a,b \in \mathbb{N_+} $ such that $\frac{a^2+b}{a+b^2}=n.$
5 answers
30 votes
1k views
8 bookmarks
Is there a closed-form solution for $\sum_{n=1}^{\infty} \sum_{m=1}^{\infty} \frac{1}{nm(3n+m)}$?
4 answers
29 votes
2k views
12 bookmarks
$f(ax)=f(x)^2-1$, what is $f$?
3 answers
27 votes
2k views
15 bookmarks
Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?
3 answers
23 votes
617 views
14 bookmarks
Black and white shirts puzzle
1 answers
20 votes
779 views
5 bookmarks
Computing the exact value of $\sum_{n=1}^\infty \left(\frac{2n+3}{3n+2}\right)^n$
4 answers
19 votes
1k views
15 bookmarks
Finding $\int^{1}_{0}\frac{\ln^2(x)}{\sqrt{4-x^2}}dx$
2 answers
19 votes
654 views
8 bookmarks
Closed form of $\sum_{n = 1}^{\infty} \frac{n^{n - k}}{e^{n} \cdot n!}$
2 answers
13 votes
493 views
9 bookmarks
Prove the equation $\left(2x^2+1\right)\left(2y^2+1\right)=4z^2+1$ has no solution in the positive integers
1 answers
12 votes
390 views
6 bookmarks
On the infinity of $\{p\in \mathbb {N}:\exists n\in\mathbb{N}~p| \left \lfloor{r^n}\right \rfloor\}$
1 answers
11 votes
185 views
5 bookmarks
Proving $\sum_{n=1}^{99}\frac{\sqrt{n+1}-\sqrt{n}}{2n+1}\lt\frac9{20}$
2 answers
10 votes
408 views
5 bookmarks
On the summation $\sum \limits_{n=1}^{\infty} \arctan \left ( \frac{1}{n^3+n^2+n+1} \right )$
2 answers
9 votes
577 views
4 bookmarks
Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$
3 answers
8 votes
1k views
5 bookmarks
maximum of monic polynomial on unit circle is 1 implies $p(z)=z^n$
1 answers
8 votes
1k views
4 bookmarks
What are the positive integer solutions to $x^2-x+1 = y^3$?
1 answers
8 votes
309 views
5 bookmarks
Dominating sets in tournaments; is $2^{n+1}-2$ tight?
1 answers
7 votes
196 views
7 bookmarks
$\sum_{k=0}^\infty\frac{ (-1)^{\left\lfloor\frac kn\right\rfloor}}{k+1}$
2 answers
4 votes
148 views
2 bookmarks
Proving a much stronger version of AM-GM for three variables
2 answers
4 votes
199 views
2 bookmarks
Prove $a^2+b^2+c^2=x^2+y^2+z^2$ given that $a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2$
2 answers
2 votes
122 views
1 bookmarks
Nice power sum inequality $ab(a-b)\leq a^{ab}-b^{ab}$ for $a+b=2$
1 answers
2 votes
132 views
1 bookmarks
Proving the quadrilaterals cyclic