I know that if $({t\over p})=1$, then $t$ is a quadratic residue, which means that $x^2 \equiv t$ mod p has solutions. So is there any skills or methods that I can use to solve the equation given a prime $p$ and $({t\over p})=1$? Thanks a lot!
Given a prime $p$ and number $a$, how do I find the smallest $n$ such that $n^a\equiv 1 \pmod p$? Is there a non trial-and-error method?  Edit: obviously removing $n=1$!
No sound after upgrade to 18.10, only a dummy device is shown After I updated to Ubuntu 18.10 my sound device isn't recognized anymore. Only a dummy device is shown.  I have an onboard Intel device:  lspci -nnk | grep -A2 Audio 00:1b.0 Audio device [0403]: Intel Corporation 7 Series/C216 Chipset Family High Definition Audio Controller [8086:1e20] (rev 04)     Subsystem: Intel Corporation 7 Series/C216 Chipset Family High Definition Audio Controller [8086:2036]     Kernel driver in use: snd_hda_intel     Kernel modules: snd_hda_intel   The command pacmd list-cards does not show any devices:  :~$ pacmd list-cards 0 card(s) available.   This message in /var/log/syslog might have to do something with the problem:  Oct 19 21:02:06 MyComputerName pulseaudio[14331]: E: [pulseaudio]  backend-ofono.c: Failed to register as a handsfree audio agent with  ofono: org.freedesktop.DBus.Error.ServiceUnknown: The name org.ofono  was not provided by any .service files   Does anybody have the same issue? How can I fix this? Smooth option sometimes produces incorrect arrow tips in PGFplots It seems that the smooth option applied to lines sometimes effects the arrow tips and produces incorrect results.  No problem with vertical lines, but any other seems to have a problem. Is this a known bug, or is there a reason why the smooth should not be applied to straight lines?  Updated: to show problem does NOT occur with TikZ, and problem also occurs with curves if smooth option is applied.  \documentclass{article} \usepackage{pgfplots} \begin{document}  \tikzstyle{MyStyle}      =[-&gt;, black, ultra thick,       ] \tikzstyle{MyStyleSmooth}=[-&gt;, black, ultra thick, smooth]  \begin{tikzpicture} \begin{axis}     % 'smooth' option seems to have no effect on lines '1' and '2'     \addplot [MyStyle      , green ] coordinates{(0,0) (0,1)} node [above] {1};     \addplot [MyStyleSmooth, blue  ] coordinates{(1,0) (1,1)} node [below] {2};     %     % But, can't seem to have the 'smooth' on lines, '4', '5' and '6'     \addplot [MyStyle      , orange] coordinates{(2,0)   (3,0)   } node [right] {3};     \addplot [MyStyleSmooth, red   ] coordinates{(4,0)   (2,0.5) } node [below] {4};     \addplot [MyStyleSmooth, red   ] coordinates{(2,1)   (3,1)   } node [left ] {5};     \addplot [MyStyleSmooth, red   ] coordinates{(3,0.8) (2,0.8) } node [right] {6};      % Similar problem with curves: "non-smooth" is ok, "smooth" is not     \addplot[MyStyle,       mark=none, domain=0:1,samples=50, blue] (x,x*x+1);     \addplot[MyStyleSmooth, mark=none, domain=0:1,samples=50, red ] (x,x*x+2);  \end{axis} \end{tikzpicture}  \begin{tikzpicture} % These are all fine     \draw [MyStyle      , green ] (0,0)   -- (0,1)    node [above] {1};     \draw [MyStyleSmooth, blue  ] (1,0)   -- (1,1)    node [above] {2};     %     \draw [MyStyle      , orange] (2,0)   -- (3,0)    node [right] {3};     \draw [MyStyleSmooth, red   ] (4,0)   -- (2,0.5)  node [below] {4};     \draw [MyStyleSmooth, red   ] (2,1)   -- (3,1)    node [right] {5};     \draw [MyStyleSmooth, red   ] (3,0.8) -- (2,0.8)  node [left ] {6}; \end{tikzpicture} \end{document} What is object slicing? Someone mentioned it in the IRC as the slicing problem. Is it possible to play FIFA 2015, 4v4 on 2 Consoles? I've the following situation: My friends and I, we're 8 in total, want to play Fifa 15 4v4. I know that the Playstation 4 just supports 4 controllers and thats why we think about a 2 console + 2 TV's setup, so 4 players per console.   So my question is: Is it possible or is there a game mode available were we could play such a setup?  Update: After I got the first answer I've to add that I know that the only way to play on 2 consoles would be through the psn online features. So we did not plan to play on Lan. We just want to sit in the same room with 2 consoles and play against each other over psn. When I watch the news I've noticed that the Gallup polls for things like presidential elections have [I assume random] sample sizes of well over 1,000.  From what I remember from college statistics was that a sample size of 30 was a "significantly large" sample.  It was made to seem that a sample size over 30 is pointless due to diminishing returns. Scale camera to fit screen size unity My background and gameobjects are 2d sprites not UI images ,I want to know how to make my background scale with screen size and positions of 2d sprits on it don't change after building game (webGl) like scale canvas with screen size and anchor points in UI elements .  Before building the game   After building Clicking to reload an updated answer removes the code snippet buttons and removes syntax highlighting Problem with gummy-bears being too much like jelly I've been trying a simple recipe I found on the internet, which is a simple recipe consisting mostly of gelatin.  The problem is that the end result is basically just a fruit-flavoured jelly (Jell-O?), rather than the more chewy gummy-bears (Haribo) style of jelly confectionery.  Can anyone suggest what I need to do to make them less springy and more chewy.  It's all difficult to articulate!  Here's what I used for the first test-batch:   12 tbsp sugar 12/3 cup fruit juice 8 tbsp Golden Syrup 8 tbsp gelatin   soften the gelatin in 1/2 cup of cold water. place sugar, syrup and the juice in a pan and gently heat until sugar dissolves. Stir in the gelatin and stir until dissolved. Pour into moulds and wait until set.    Thanks This question led to a new package:      I'm trying to make some good-looking numbers in a circle, using the simple command:  \textcircled{1}   However, the circle is misaligned vertically with the number, and look a bit sloppy:    Any suggestions how can I adjust the vertical alignment so that the numbers look more centered w.r.t to the circles? Or, if that's not an option, what other ways to achieve the same results are possible?  I will use those only for numbers, and in very few places, so manual adjustment per glyph is an option.  I'm using pdfLaTeX with Computer Modern, if that matters. Every principal ideal domain satisfies ACCP. How do I Enqueue styles/scripts on Certain /wp-admin Pages? I have two simple functions that load stuff using  and , something like these:  function admin_custom_css() { wp_enqueue_style( 'stylesheet_name', 'stylesheet.css') };   function admin_custom_js  { wp_enqueue_script( 'javascript_file', 'script.js') };   ... and a few admin pages, created with  and   function my_menu() {    add_menu_page('Page 1', 'bar', 'something', 'else', 'foo');    add_submenu_page( 'theme_menu', 'Subpage 1', 'Subpage', 'something', 'else', 'foo');  } add_action('admin_menu', 'my_menu');    How do I load my two functions only on these pages?  Right now I'm using:  add_action('admin_init', 'admin_custom_css' );  add_action('admin_init', 'admin_custom_js' );     But it loads my files on every admin page, which is not nice at all.  Can I do this via one simple line in functions.php or have to enqueue them within my pages separately (I prefer the first option strongly, since I'd have to edit a lot of admin-page-creating-functions).  Thanks! Prove that $\liminf x_n = -\limsup (-x_n)$ Enabling Nvidia driver messes up splash screen Removing nodes from an XmlDocument Avoiding NullPointerException in Java I updated LyX to 2.3.0-1, and found that LyX was displaying all the "-" characters in Math Mode as "\lyxminus". No such problem occurs when entering outside of Math Mode. LyX also seems to have no problem compiling to TeX, and the PDF output looks normal.  I removed and re-installed LyX, and this issue was still there.   Does anyone have any ideas on what might be going on? I am using Linux Mint 18.2 Sonya.  Note: I previously saw this question ask about the same thing, but the author appears to have deleted their post: In Minecraft, there are a lot of cool sounds. I decided to find there location and move them to my desktop. I have Ubuntu, and if when I remove them from that folder will Minecraft be unable to play them or is it smart enough to figure out that they are gone and download them again. Before minecraft was installed, it had to download the files. I even moved my favorite song (creative 6) from the sounds. The sounds are not labeled and have seemingly random names like b0b12118a97ddd733a50e9382e91a21652568641 and how will I know what to call them that will be recognized without digging through the index if Minecraft fails to download them? Or do I not have to worry because it will download them again upon launch?  Note: Why does it not label them and call them random names? Transformer, how the primary current is adjusted to be equal to the secondary load (without considering magnetizing current)? I am happy to always not understand how does a transformer works ... One answer give me 10 questions ... (So I suggest you to not answer to this question, if you do not want to have more questions :D)  Here is the circuit :     So I put the "coupling" factor to 1, in order to have no leakage inductance and I set the value of the inductors very high in order to have a very low magnetizing current. So the primary current is approximately equal to the secondary current. My question is the following : How the primary current can reach an equilibrium to be equal to the secondary load current ? I will not accept answer which tells Pout is equal to ... So Pin is equal to Pout... There is something happenning into the transformer ...   Thank you very much and have a nice day ! Flying EU to UK to EU. Can I get duty free alcohol? On the 20 of March this year I will be flying from Ireland to the UK and then on the another EU country.  Can I buy duty free alcohol (as in alcohol with no tax) leaving the UK ? I'm looking for a fantasy book I read about 10 years ago. I don't remember a lot of it, but there are a few things I still know:   The setting was in medieval times. There was no traveling dimensions. I can't recall whether there was magic or not. It wasn't on Earth, but on some invented world. I believe it was a trilogy, with a focus on the son of some nobility. The goal for the characters was to collect a certain number of stones or gems (I believe there were 5 of them), all in certain colours. Every stone has a certain power attached to it. I believe it started out with one or two characters, but the group grew and every character had a certain colour stone at the end. What is important about the gems is that they are unique. It's not part of a bigger magic system, but they are artefacts from somewhere.   There are some minor incidents I can recall vividly:   They build up a fellowship with some stereotypical fantasy builds: an old school fighter, a minstrel, a female archer and probably more. At one point, they mention that if one of the guards in a country falls asleep on duty, he will be kept awake by his garrison/brothers in arms for seven days. At some point the minstrel falls asleep, and the old fighter teaches him how to stay awake. They travel through a forest full of leeches and other insects to reach one of the stones. Also, I seem to recall there was a member of an underground evil organisation among the nobility, who tried to poison someone and were able to do that because they built up an immunity to the poison.   Does anyone has a clue what this series might be?   Suggestions by kind people, but not what I'm looking for, are:   The Seventh Tower Deltora Quest Diadem Westria Sword of Heavens series