Order of $xy$ when $\gcd(o(x), o(y)) = 1.$
Order of product of two elements in an abelian group
How to open a terminal from within Atom? I'm currently working with Atom, and sometimes I want to open a terminal on the directory my working file is. To do this, I usually have to open the folder in nautilus (right clicking the file in atom) and then I open a terminal on that directory from nautilus (right click).  I wonder if there is a way to open the terminal in the file directory without having to open nautilus first. Saving Arduino sensor data to a text file Is it possible to only allow specific packages updates from a PPA Let us say I have added a PPA that has X package that I want but it also has Y package that I do not want to use or receive updates from. How can I, from the same PPA, receive updates for a specific package but deny updates from the same PPA for other packages.  A step by step example would be good since this has happened to me in several PPAs that have a particular package I want but also add a whole bunch of others that I do not yet want to update. Preventing console window from closing on Visual Studio C/C++ Console application Login not redirecting back to page where login link was clicked if account created Halo particles don't render in Cycles How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$? Show that $$n! \leqslant \left(\frac{n+1}{2}\right)^n \quad \hbox{for all } n \in \mathbb{N}$$  I know that it can be done by induction but I always find line where I do not know what to do next. Things to focus on in a model lesson A model lesson is a usual element in interviews for the faculty level positions. Normally this is not a full lesson but a 15-minute version which is performed in absence of actual students for just a few professors from a hiring committee. It is supposed to demonstrate "your teaching style", but by design this is clearly a different enterprise: you should "act normal" doing "the same" things    in a different time-frame,  for a different audience,  with completely different motivation and  under exorbitant cost of failure.   Having said this, I also acknowledge the model lesson as indeed a much needed element of the interview, which helps to assess a candidate's set of relevant skills.  The question is how one can ideally prepare to give such a model lesson. Putting aside obvious things like "structure of the talk," "clear slides," "projection of the voice," and "body language", which normally should be already trained by experience, are there specific things that should be taken into account for the model lesson only? What about techniques like jokes, questions to the audience (e.g. how many of you are familiar with the definition of the derivative), work in pairs, which you probably use in a real classroom &mdash; is it a good idea to demonstrate them in a room full of senior professors? I am a little confused. Event handler not working on dynamic content Failed to resolve version for org.apache.maven.archetypes A subring of the field of fractions of a PID is a PID as well. Let $A$ be a PID and $R$ a ring such that $A\subset R \subset \operatorname{Frac}(A)$, where $\operatorname{Frac}(A)$ denotes the field of fractions of $A$. How to show $R$ is also a PID?   Any hints? Can the relative pronoun "whose" be used for animals, things and countries? When I was a student of English as a foreign language, more years ago than I care to count, I was taught that the relative pronoun “whose” could only be used for human beings, i.e., when someone possesses something.   My teachers were native speakers from England, then.   Since that time, I’ve seen “whose”, as a relative pronoun, used in several contexts where no human beings are mentioned, e.g. with animals, objects, countries, abstract nouns, etc, in American newspapers and magazines. Unfortunately, I can’t remember any of the sentences and cannot give examples.  What is acceptable in written and spoken English, and what isn’t, concerning the use of “whose” ? How to gracefully handle files that exceed PHP's `post_max_size`? I have a WordPress install on a dedicated server with decent memory (upwards of 8GB).  The WordPress install includes many plugins - 50 active plugins. Most important to note is the  plugin to make WordPress multilingual. The theme is .  The stack is LAMP - CentOS 6.3, Apache 2.4.4, Percona MySQL, PHP-FPM.  I have been quite stupid, and didn't set up a test or staging server.  Everything was running fine till I updated to WordPress 3.8, and also updated several plugins at the same time.  I didn't pay attention at the time, but all my widgets got messed up, and so did any sort of navigation etc.  I enabled error_log for a bit, i.e.  ini_set('log_errors',TRUE); ini_set('error_reporting', E_ALL); ini_set('error_log', dirname(__FILE__) . '/error_log.txt');   This resulted in an immense file - basically the error_log grows by about a GB every 4 minutes or so.  The primary error I found in the error log was database server disconnect, better known as      MySQL server has gone away   The first priority was to patch the problem. So I installed  plugin. This mostly, though not completely solved the issue. Many of the widgets came back.  However, the special (non-English) characters are all messed up (converted to question marks). I tried to fix this by opening wp-mysql-ping.php and commenting out   if ( !DB_CHARSET &amp;&amp; version_compare(mysql_get_server_info($this-&gt;dbh), '4.1.0', '&gt;='))                                     {                                         $this-&gt;query("SET NAMES '" . DB_CHARSET . "'");                                     }   Didn't help.  Besides, the plugin is not a permanent or complete solution. So leaving the site in this messed up state, I started working on other possibilities:  As suggested at , I edited my.cnf to add  wait_timeout = 60   Didn't help.  Also added caching to my.cnf  query_cache_type = 1 query_cache_limit = 8M query_cache_size = 512M   Didn't help.  (and yes, I restarted mysql every time I edited my.cnf)  Also tried the method : In wp-db.php before  $this-&gt;select( $this-&gt;dbname, $this-&gt;dbh );   I added  $this-&gt;query("set session wait_timeout=600" );   Didn't help.  I'm at my wit's end. Please help! As the question states... In Windows 7 with a single screen, you can drag a window to the right and a window to the left to maximize them both at half the screen, letting you quickly and neatly see two windows simultaneously.  If I have 2 monitors, is there a way to do this with 4 windows, where each monitor gets 2 windows split across each screen? Problem with Refsection I can't seem to get the reference within my {refsection}.  \documentclass[a4paper]{article}  \newcommand{\myparagraph}[1]{\paragraph{#1}\mbox{}\\}  \usepackage[     backend=bibtex,     isbn=false,     url=false,     doi=false,     eprint=false, ]{biblatex}  %Point to the bibliography db \addbibresource{mybib.bib}  \begin{document}  \include{myparagraph}  \end{document}   My paragraph file  \myparagraph{\fullcite{dante1320}} \begin{refsection}  \cite{manzoni1827}  \printbibliography[heading=subbibliography] \end{refsection}   I get the first citation (dante1320) right, but the second prints as [manzoni1827]. I don't get any error when I run Bibtex concerning the missing reference. But I got it when I run Latex: LaTeX Warning: Citation 'manzoni1827' on page 2 undefined on input line 5. Can we make a Vpn server run on Android. Can applications do this? If yes, which protocols are supported and is this a good idea to use such apps? If not, what are some issues that we may face? I want to enter the following folder in the terminal:  Milano, Torino (Jan)-Compressed   How should I write the command cd to enter this directory?  Spaces and several other special characters like \, *, ), ( and ? cause problems when I try to use them in the command line or scripts, e.g.:    $ cd space dir bash: cd: space: No such file or directory  $ cat space file cat: space: No such file or directory cat: file: No such file or directory  $ cat ( bash: syntax error near unexpected token `newline'  $ echo content &gt;\ &gt; ^C  $ ls ? (  )  *  ?  \   How do I enter file or directory names that contain special characters in the terminal in general? How to use "fit" to frame the nodes and labels Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square. Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square. My work: $2xy\mid x^2+y^2-x \implies x^2+y^2-x=2xy\cdot k$ So,$x^2+y^2+2xy-x=(x+y)^2-x=2xy \cdot (k+1)$ And,$x^2+y^2-2xy-x=(x-y)^2-x=2xy \cdot (k-1)$ I found that for $x,y$ both odd, no solution exists. For $x$ even, and $y$ odd,no solution exists. Solution exists only for $x$ odd, $y$ even and $x$ even and $y$ even solution exists. Cannot do anything more. Please help!