I use LaTeX for writing books. I would like to extend my working environment and, I was wondering if it is possible to read (or much better - edit) tex files containing text only on an ipad? I know that there are a few LaTeX editors for the ipad out there. But, I use Aquamacs as my main writing editor and, LuaLaTeX as the writing medium. I do not want the file format changed in any way. Does anyone have any ideas? I thought of using say, Dropbox and then being able to open the file on the ipad, add a sentence or two, correct a few spelling errors say then, send the file back to Dropbox. Is this possible?
Is there a (La)TeX distribution running on iPad?
I want to show without using Sylow theorem that     Any group of order $2p$ has a subgroup of order $p~$($p$ being a prime)   My attempt: Since $|G|=2p,$ even $\exists~a\neq e\in G$ such that $a^{-1}=a.$ Then $H=\{e,a\}\leq G.$ Let $S$ be the set of all left cosets of $H$ in $G.$ Now $S$ forms a group w.r.t. the composition $g_1Hg_2H=(g_1g_2)H.$ The mapping $\sigma:S\to G:gH\mapsto g$ is an $1-1$ homomorphism. Then $S\simeq\sigma(S)\leq G.$ Thus $G$ has a subgroup of order $p.$  Please tell me whether I'm right!     I'm skecptical as I didn't use that $p$ is prime. data.table and table unexpected behavior How did Toru and Koji pass the entrance exam in My Hero Academia? I have seen some comments and speculations about the robot having an off switch or whatever. But I want to know if there is any source material or comment from the author on how they managed to pass the exam.  I have only seen the actual author's comment on Mineta:     But I was wondering if there are author notes for the other characters. The impression that I got from the  films was that if  was successful, most of the world was going to suffer greatly. Basically everyone would serve Voldemort as slaves or die. So what's the point of serving someone who's probably going to ultimately end up betraying and/or enslaving you? I know the  hated , but is that really enough to justify tearing down Wizard society? Why exactly do the Death Eaters serve Lord Voldemort? Fear? Is the post-Voldemort world not that bad? (I for one welcome our ) If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$. Prove if $\operatorname{ord}(a)=m$, $\operatorname{ord}(b)=n$, and $\operatorname{gcd}(m,n)=1$, then $\operatorname{ord}(ab)=mn$.   I was reading this and was thinking how this proof would look like. I tried to do it and am not sure if this is correct. Here is what I did:  If $a$ and $b$ commute then $(ab)^{mn} = a^{mn} * b^{mn} = (a^m)^n * (b^n)^m = 1 * 1 = 1.$ So $ord(ab) | mn$.  Now, take $k = \operatorname{ord}(ab) = m^\prime * n^\prime$ where m' is relatively prime with $n$ and $n'$ is relatively prime with $m$. By the result above $m' | m$ and $n' | n$. Now we have $((ab)^k)^{m/m'} = 1$ since $(ab)^k=1$. But on the other hand, by the commutativity:  $$((ab)^k)^(m/m') =$$  $$((ab)^(m' * n'))^(m/m') =$$  $$ a^{n'm} * b^{n'm} = $$  $$(a^m)^{n'} * b^{n'm'}=$$  $$b^{n'm'} = 1$$  This implies that $n' * m'$ is divisible by $n$. But $m'$ is relatively prime with $n$, so we must have $n' = n.$ By symmetry, $m' = m$. So $ord(ab) = mn$.  Just to say this again, I want to prove if $a$ and $b$ commute and $m$ and $n$ are relatively prime then   $$ord(ab)=mn.$$   The comments are vague. I guess this must be the answer then and there probably is not another way to do this. How do I prove the sequence $x_{n+1}=\sqrt{\alpha +x_n}$, with $x_0=\sqrt \alpha$ converges? ( boundedness?) Author information column wise I am using authblk package and I want to achieve following output using this package. Error handling in C code Every finite group is isomorphic to some Galois group for some finite normal extension of some field. Prompted by a  I was pondering the idea of bikes with variable gearing (derailleur or otherwise) but without the ability to freewheel. Have such bikes ever been widely used?  They would appear to share many of the advantages and disadvantages of fixies but be better at handling hills (up and down) while being more complex. Why was Arcanine with the Legendary Birds in Veridian City in Pokémon Origins? In Pokémon Origins, Red sees a image with the three legendary birds and Arcanine.     Why was Arcanine there? I mean, he's 'The Legendary Pokemon' but not a legendary Pokémon. In , there is a comment by  on the answer that Arcanine was originally a legendary Pokémon:     "...Nintendo first gave Zapdos, Articuno and Arcanine as the legendary trio. But they removed Arcanine as it would have been awkward. Two birds and a dog, huh!..."   This still does not add up because Pokémon Origins was created a while after they removed Arcanine. Any thoughts? Why does the dock appear on the left when my screen is locked? The dock doesn't work correctly after I enter my password, either. Is it bad behavior to add filler words such as "so", "um" in business speak? What is the most ruby-ish way of accessing nested hash values at arbitrary depths? I created a thick glass bottle and duplicated the interior faces to make a new object to create the liquid inside.   I went in the edit mode, selected the faces I wanted to copy and duplicated them with ShiftD. Then I pressed P to  separate the duplicated faces.   Now I try to make a duplicate of that liquid to make it flow out of the bottle, and I simply need the duplicate of one face of it. So I go to edit mode and do as I did to make the liquid from the bottle faces... but as soon as I'm back to the object mode and I want to move the duplicated faces, every thing moves with it...   I played around and tried things, and while doing so I realized that if I dupe the liquid object in object mode using ShiftD and press 0 to place it where the original is, they move together if I duplicate it and place it somewhere else so that they are separated.   Also if I pick one of the two separated objects and make it intersect with the other one, release my left mouse button to place it there, and then try to move it again, they both move together, but not at the same speed.  I really don't understand what is going on and I'm sure it's really badly explained, so what I'll do is make a screen capture of my Outliner and record the behavior of the objects and upload those to help you understand. When do you use “learnt” and when “learned”? Is learnt UK English and learned US? Is it that simple?  I’m used to using learnt, but my US spellchecker says it is wrong. Why aren't variables declared in "try" in scope in "catch" or "finally"? In C# and in Java (and possibly other languages as well), variables declared in a "try" block are not in scope in the corresponding "catch" or "finally" blocks.  For example, the following code does not compile:  try {   String s = "test";   // (more code...) } catch {   Console.Out.WriteLine(s);  //Java fans: think "System.out.println" here instead }   In this code, a compile-time error occurs on the reference to s in the catch block, because s is only in scope in the try block.  (In Java, the compile error is "s cannot be resolved"; in C#, it's "The name 's' does not exist in the current context".)  The general solution to this issue seems to be to instead declare variables just before the try block, instead of within the try block:  String s; try {   s = "test";   // (more code...) } catch {   Console.Out.WriteLine(s);  //Java fans: think "System.out.println" here instead }   However, at least to me, (1) this feels like a clunky solution, and (2) it results in the variables having a larger scope than the programmer intended (the entire remainder of the method, instead of only in the context of the try-catch-finally).  My question is, what were/are the rationale(s) behind this language design decision (in Java, in C#, and/or in any other applicable languages)? Attributive or Possessive noun: the Dell Company's staff. or the Dell Company staff? In the following is it better to use a possessive noun with an apostrophe or an attributive noun without an apostrophe?     The following list details the assumptions that have been made in   conjunction with the Dell Company’s staff.   Or      The following list details the assumptions that have been made in   conjunction with the Dell Company staff.   Assume Company is the name of a company, such as Dell. Samba+Windows: Allow multiple connections by different users? I have a machine running Ubuntu with Samba that I use to share stuff with my family's Windows machines in our local network.  Currently they access a share for movies/music/etc with one user.  I want to connect them to another share as a different user (for example, user "goytacaz").  When I try connecting to this new share, Windows gives me "Error 1219" and complains about multiple connections by the same user.  How do I get my machine to accept multiple connections by the same user? If every prime ideal is maximal, what can we say about the ring? Suppose $R$ is a ring and every prime ideal of $R$ is also a maximal ideal of $R$. Then what can we say about the ring $R$?