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comment Kloosterman Sums and Lattice Hyperbolas
@GregMartin this is how I feel about the blog I am reading :-(
Aug
26
comment Large regions of the plane $(x,y) \in \mathbb{Z}^2$ with no relatively prime points: $\mathrm{gcd}(x,y) > 1$
this is perfect. the number you get using Chinese Remainder Theorem get pretty large, but all I asked is some way to assure me the existence of large holes.
Aug
26
comment Large regions of the plane $(x,y) \in \mathbb{Z}^2$ with no relatively prime points: $\mathrm{gcd}(x,y) > 1$
What do you mean pairwise distinct? We have infinitely many prime numbers, so it's good. I am guessing you mean distinct along each row or each column ?
Aug
25
comment Groups of order $8n$ have at least five distinct conjugacy classes
@JasonDeVito OK. There could be any odd number of Sylow 2-groups, all conjugate to each other, which intersect each other in interesting ways.
Aug
25
comment Groups of order $8n$ have at least five distinct conjugacy classes
@JasonDeVito Third Sylow theorem says the maximal Sylow $p$-group is normal. I stand corrected.
Aug
24
comment Intuition behind the construction of Young Symmetrizer
@anon sorry I have been occupied.
Aug
23
comment Intuition behind the construction of Young Symmetrizer
hep.caltech.edu/~fcp/math/groupTheory/young.pdf
Aug
16
comment Area of the lattice generated from $(n, n\sqrt{2} \mod 1)$
@LeeMosher I start out with the line $(t, t \sqrt{2}) \in \mathbb{R}^2$ and mod the y-coordinate by $1$, $(x,y) \mapsto (x, y \mod 1)$ so it's wrapping around a cylinder $\mathbb{R}\times S^1$. Additionally $t \in \mathbb{Z}$ so although I started with a line in the plane, it really looks like a 2D lattice on the cylinder.
Aug
16
comment Moebius band not homeomorphic to Cylinder.
@ThomasAndrews sure I can; I am taking the closure of a subset of the cylinder/Mobius band in the relative topology.
Aug
15
comment Proof of $\sum_{d|n} {\tau}^3(d)=\left(\sum_{d|n}{\tau}(d)\right)^2$ (not standard proof)
Also $\sum k^3 = \left( \sum k \right)^2$. Concidence?
Aug
15
comment Moebius band not homeomorphic to Cylinder.
@PyRulez My constructions are fine. If the two spaces where homeomorphic, we could map one meridian circle to the other $S^1 \subset X \leftrightarrow S^1 \subset Y$. Since both spaces fiber over the circle, we can take a closed interval over each point in $S^1$. The result is a closed cylinder on the one hand and a closed Möbius band on the other.
Aug
15
comment Area of a Random Polygon
I don't think the exact formula is a very exciting thing to compute. There are some interesting formulas in the large $n$ limit. See the papers of John Pardon. arXiv:1110.5656 Central limit theorems for uniform model random polygons.
Aug
15
comment Without using Heegner-Stark-Baker, $\mathbb{Q}(\sqrt{-11})$ has class number $1$.
Possibly related Dense Packings from Algebraic Number Fields and Codes Shantian Cheng
Aug
13
comment Does $\cos (\pi/5)$ belong to $\mathbb{Q} (\sin(\pi/5))$?
Somehow we should exploit: $\cos \frac{\pi}{5} = \sqrt{1 - \sin^2 \frac{\pi}{5}}$ or something. I been looking at these proofwiki.org/wiki/Quintuple_Angle_Formulas
Aug
11
comment Number of irreducible quadratic polynomials over a finite field
I like your use of "invisible ink" - it's great pedagogical tool.
Aug
11
comment Number of irreducible quadratic polynomials over a finite field
In $\mathbb{F}_2$, there are only 4 possibilities $x^2 , x^2 + 1=(x+1)^2, \color{blue}{x^2 + x + 1}, x^2 + x = x(x+1)$
Jul
29
comment Can the numbers $2^m 3^n$ have an infinitely long arithmetic sequence?
See it's not so easy? Dirichlet's theorem was my motivation for this problem. As for the comments above, proving the natural density is 0 might also be hard.
Jul
25
comment Can $O(\sqrt{x})$ be considered $o(x)$?
@user251257 Oh my. What an important question. I guess $\boxed{x \to \infty}$, but $x \to 0$ could be important.
Jul
19
comment Product of complex numbers $m+in$ with $0 < m,n \leq N$
@zardo if you can find Stirling approximation in that case then please write an answer
Jul
18
comment Explaining Mathematical Modelling to a nonmathematician
have you considered Math Educators Stackexchange