I found the following question in my Galois theory book:     Let $F$ be a field with $|F|=p^2$ for some prime $p$. Show that $a^2=5$ for some $a\in F$, and generalize this statement.   My supposed proof is this: Let $a$ be a root of $x^2-5$, and suppose it is not already in $\mathbb F_p$. Then $\mathbb F_p(a)$ is a degree $2$ extension and so by uniqueness of fields of a certain order, $F=\mathbb F_{p^2}=\mathbb F_p(a)$ . Q.E.D.  This seems to me like it is a bit too easy and we didn't really do any work, and if this were to work, then we can generalise it to     Let $|F|=p^n$, and suppose $f$ is an irreducible polynomial over $\mathbb F_p$ of degree $n$. Then it has a root in $F$.   To me this sounds a bit too good to be true, but since I'm relatively new to field theory I'm not too sure. Is this correct?
maybe that's an idiot question. Given a finite field $k$ and some irreducible polynomial $f(x) \in k[x]$, then $k_f \cong k[x]/(f(x))$? I know that it's true if $k$ is the prime field and I think that the statement is not true for general finite fields, however I could not find any counter example.  Thanks in advance.
What websites or other resources do users of Blender have available to them to report bugs or problems with the program?  I would like to get this issue cleared in Q&amp;A format so that we can link new users with bug-report-style questions to this post. I'm using a \chapterstyle{tandh} because I want my chapters numbered. In order to get a References chapter numbered as well I used the following code:  \renewcommand{\bibsection}{% \chapter{\bibname}}   That worked fine, I got my References chapter numbered!!   But now, in order to get my references in a author-year style I'm using the natbib package. Seems like the package ignores my code and the References chapter is not numbered anymore.  Can someone help me? I want to install the PyCharm IDE by JetBrains for Python (free community edition).  I managed to , but I do not know how to install it. Can you please help me? Does a creature with Lifelink provide lifegain equal to its power, or the defender's toughness? TikZ externalization with absolute path and MiKTeX distribution This code:  \documentclass[11pt,openright]{book} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \usepackage[british]{babel}  \usepackage{tikz} \usetikzlibrary{external} \tikzexternalize[prefix={"C:/Users/MyName MySurname/Documents/LaTeX/Figures/"}]  %\tikzexternalize[prefix={Figures/}]   \begin{document} \begin{tikzpicture}     \draw (0,0) circle (1cm); \end{tikzpicture} \end{document}   gives me the error:     ! I can't write on file `"C:/Users/MyName   MySurname/Documents/LaTeX/Figures/MyMWE-figure0.md5"'.   I'm working with Windows 10, MiKTeX 2.9 distibution.  Following the advice Tarass gave me on a comment of this question:  and as indicated here:  I've registered a user-managed TEXMF directory but I still get the same error.  With \tikzexternalize[prefix={Figures/}] all works perfectly but, since I'm using LyX, the files are stored in a LyX temp dir, hence I loose them when I close the program (making externalization useless), so I need to use an absolute path. TSA broke a lock for which they have a master key. How can I claim compensation? Can someone identify the fonts used in the words "nature methods" in the following image?    I think that the word "nature" is in Times or Times New Roman (?) but can't figure out what font the word "methods" is in.  Any ideas? ASP.NET Stress Testing Is there a way to test an application where you simulate a hundred different clients connecting to a IIS server and asking the same data? At the customer where our project is running they have 400 computers and they often do stress tests with all computers. I on the other hand have only got my laptop... (and a development server).  (In my case the data is asked through a WebORB Gateway). Can we access class properties dynamically with Object class? Is it possible to access Apex class properties dynamically? While we can create Object's, and assign any other class to an Object, I'm not sure how I can access the properties of these Object's. Can anyone provide some documentation or references to code which would allow me to do this?   Example:  public class XYZ {    public string s1 { get; set; }    public string s2 { get; set; } }  XYZ testXyzObj = new XYZ(); Object obj = testXyzObj;  // Method does not exist or incorrect signature: [Object].get(String) String s1 = obj.get('s1'); I'm trying to figure out a good workflow for developing scripts and add-ons in Blender. Here's what I'm currently doing as I try my luck with a PyNode add-on:   Open blender Create a text editor panel Open my script (external text file) Edit my script in a nice external editor Reload the script Save the .blend file Run the script   Now that I can see what my code does, this Blender instance has been modified, so I can't (make changes to my script and) run my script again. So I do this:   Close blender Open blender with the .blend from step 6 and repeat steps 4-7, over and over and over..   Is there a better workflow for this sort of thing? Rational solutions of $y^2 = x^3 - x$ Can the Force be used to fly? Clarification on maps in Salesforce I know this might be a very basic question but i'm pretty confused by this:  Map&lt;Id,Account&gt; accountWithOpportunities =      new Map&lt;Id,Account&gt;([SELECT Id,(SELECT Id FROM Opportunities) FROM Account]);   I have no clue on to where the Opportunities are relevant at all in this map and how they are stored or can be accessed?   Can anyone clear this out for me? I would like to increase the size of pretty much every headlines, so that it is more prominent than the normal text.  I read about the  package, but can't seem to find good example how to use the package.  Using Gonzalo Medina does in fact change the font size, however, it changes the default font as well.  Before:    After: How can I include custom post types on a tag page? I'm using custom post types, but they don't appear on tag pages along with regular posts and i'd like to include both standard and custom post types on tag or category pages. What would be required before the loop to include all posts? (including custom type). Updated: To add, I found this code , which worked perfectly for the first part: add_filter('pre_get_posts', 'query_post_type'); function query_post_type($query) {   if ( is_category() || is_tag() &amp;&amp; empty( $query-&gt;query_vars['suppress_filters'] ) ) {     $post_type = get_query_var('post_type');     if($post_type)         $post_type = $post_type;     else         $post_type = array('post','cpt'); // replace cpt to your custom post type     $query-&gt;set('post_type',$post_type);     return $query;     } }  Second question still remains though: Is there a way to allow readers to filter by post type? So either of the following would work..  example.com/tag/blue?post_type=custom example.com/tag/blue?post_type=post Why aren't the humans wearing environmental suits in Star Wars spacecraft? The word "Print" appears after every source using \printbibliography Problem after update: blue screen with only the mouse cursor Develop rich API exposing Stack Overflow functionality I would love to see an actual native iPhone app for Stack Overflow, Server Fault, Super User, etc.  I've actually developed a number of iPhone apps myself, and would certainly be interested and willing in doing the bulk of the legwork, but it would be necessary for the SO team to expose a real API, instead of simply RSS feeds.  Maybe if there's enough demand behind this, we can convince the SO team to build a rich API, which could be useful for many other applications, not just an iPhone app. I have windows 7 in Arabic. Now I dowloaded QGIS 2.14.3-2 in French.  But when I installed it shows Arabic menu/tools...  How can I change the menu language to French?