Let $p$ be a prime number ($ p \ne 2, p \ne 5$). How can I prove that this prime number divides at least one number with a decimal representation that consists only of $1$s ($111$, $1111$, etc.)
How can I prove that every prime except 2 and 5 divide infinitely many of the following integers $11, 111, 1111, ...$ ?
Bought a new battery, do I need to calibrate it? My original battery is bloated and is dying quickly after a full charge so I now bought a replacement. Do I need to calibrate this new battery using a calibration app? Given two input layers  The clip layer - an arbitrary layer (though in my case it's a float 1 band geotiff) The mask layer - a paletted raster in which every pixel is either NO DATA or a single &quot;color&quot; value, same for every pixel.  I want to create an output raster whose overall extent matches the extent of the mask layer and each pixel is either NO DATA if the corresponding pixel of the mask layer is NO DATA or the value of the corresponding pixel from the clip layer if the corresponding pixel of the mask layer is not NO DATA. I know I can mask the clip layer with a polygon, but the mask layer is a raster. Polygonizing the raster layer is possible in principle, but would result in a polygon with a lot of very short edges. Is there a direct way to do this in QGIS? I suppose there's probably a path that involves creating a new layer and using the raster calculator, but I'm hoping there's something more direct. Further complicating the matter is that the two rasters might not have the same resolution and origin. I believe this is equivalent to  in ArcMap. How to access a clicked URL in a URL handler application created in Automator I'm currently trying to modify the default URL handling behavior in OS X. I would like, when clicking on any link outside of a web browser, to copy this URL to the pasteboard instead of opening it in the default web browser – for instance, clicking a link in a Skype conversation should copy this URL to the OS X pasteboard instead of opening it in Firefox (which is currently my default web browser).  I have thought about solutions, but I’m currently unable to implement one. If I can create an application that puts URLs into the pasteboard that are sent to it, and can set this application as the default web browser, I would be able to achieve my goal.  I created an application with Automator that executes the shell command pbcopy and have set this application as my default web browser, but I didn’t get the expected result. I did some testing and I can confirm that the application runs on clicking on a link, however, I cannot get the URL passed to the application / shell script. I tried both stdin or a passed argument, but without success.  Is there a way for an application created with Automator to retrieve a clicked URL and send it to pbcopy, when that application is set as a (default) handler for URLs?  Alternatively, is there a better way to create a fake web browser that takes the input and puts it in the pasteboard than Automator? Or is there any other way that I can achieve my goal without a custom application / script? Suppose $R\neq 0$ is a commutative ring with $1$. Let $M$ be a free $R$-module. I would like to prove that $M$ is a flat $R$-module. Everywhere I have looked (mostly online) this is proved by first proving that every free module is projective, and then proving that every projective module is flat. Unfortunately, Atiyah &amp; Macdonald's "Introduction to Commutative Algebra" (Chapter 2) does not discuss projective modules. But the result that every free module is flat comes very handy in the exercises.   So my question is,     Is it possible to prove that every free module is flat just by   definitions and without appealing to projective modules?   Thanks! Asymptotics of uniformly continuous functions over $\mathbb R$ Microphone doesn't work in Hangouts I have a DELL inspiron 5537 i5 laptop with Ubuntu 14.04. When I use Google Hangouts on Google Chrome, my mic just doesn't work. When I open the secure info setting it shows that the mic is allowed.  Works in Windows.  I have tried to add the Hangouts plugin and it also doesn't work.  Is there any to solve the problem? 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. After trying to delete apache and tomcat, and now trying to reinstall apache 2, I am missing the init.d/apache2 file to start/stop my server.  I am not sure if the new install actualy worked, and my apt-get purge apache2 didn't remove everything in the first place!  How can I get the init.d/apache2 file to test if server starts / is installed properly (I had removed files and directories manually)? Android Respond To URL in Intent I want my intent to be launched when the user goes to a certain url: for example, the android market does this with  urls. so does youtube. I want mine to do that too. How can there be animals on the surface in Zion's world? It is apparently canon that  in Neo's day.  However, in the first movie, The Matrix, Morpheus tells Neo that one of the things known for certain is that humans "burned the sky" in order to deny solar engery to the machines, which in turn led to the humans who survived the War being plugged into the Matrix to provide bioelectric energy to supply the machines.  If there's not enough sunlight for solar power, how can there be enough to grow plants to serve as food for animals?  Low levels I can understand -- house plants, at least, thrive in conditions too dim for solar panels to produce cost-effective power -- but every surface scene we see in the trilogy is as dark as a cloudy night; light coming only from the machines.  That wouldn't begin to support photosynthesis, which means all animal life would starve in, at most, a matter of a few years. Forgot which email I used, can't login I forgot what email I used for my other ploxtic id: how do you find out what my email was?   The account is user:2078229. How can I create an executable JAR with dependencies using Maven? I want to package my project in a single executable JAR for distribution.  How can I make a Maven project package all dependency JARs into my output JAR? Pairwise independence of Random variables does not imply indendence Show by a counterexample that for a family $(X_i)_{i\in I}$ of random variables the independence of all pairs $(X_i,X_j)$ with $i,j\in I, i\neq j$ does not imply the independence of the family (It is enough to consider $\mbox{card}(I)=3$.).      Hello, I am searching for a simple example. The professor gave the hint that one might consider random variables which only can take two different values, but I do not know exactly what is meant.  By the way:  We call the family $(X_i)_{i\in I}$ of random variables independent, if $(\sigma(X_i))_{i\in I}$ is independent, whereat we call a family $(\mathcal{E}_i)_{i\in I}$ with $\mathcal{E}_i\subset\mathcal{A}$ independent, if for any finite subset $I_0\subset I$ and any choice $E_i\in\mathcal{E}_i, i\in I_0$, it is $$ \mathbb{P}(\bigcap_{i\in I_0}E_i)=\prod_{i\in I_0}\mathbb{P}(E_i). $$ Is there any way to get the number of pending chat request on omni channel? I have a requirement to get the number of pending chat request in the omni channel.  I have set the presence configuration capacity to 5 so that an agent can have only 5 chat requests. if a case is solved agent will get one of the pending chat request. But right now i can't see the number of pending request.     Lets say i have 10 pending request in the queue, but i don't have any numbers to see how many are pending in the queue.   Is there any way that can show the pending chat requests in the queue? How do you pass a member function pointer? I am trying to pass a member function within a class to a function that takes a member function class pointer.  The problem I am having is that I am not sure how to properly do this within the class using the this pointer.  Does anyone have suggestions?  Here is a copy of the class that is passing the member function:  class testMenu : public MenuScreen{ public:  bool draw;  MenuButton&lt;testMenu&gt; x;  testMenu():MenuScreen("testMenu"){     x.SetButton(100,100,TEXT("buttonNormal.png"),TEXT("buttonHover.png"),TEXT("buttonPressed.png"),100,40,&amp;this-&gt;test2);      draw = false; }  void test2(){     draw = true; } };   The function x.SetButton(...) is contained in another class, where "object" is a template.  void SetButton(int xPos, int yPos, LPCWSTR normalFilePath, LPCWSTR hoverFilePath, LPCWSTR pressedFilePath, int Width, int Height, void (object::*ButtonFunc)()) {      BUTTON::SetButton(xPos, yPos, normalFilePath, hoverFilePath, pressedFilePath, Width, Height);      this-&gt;ButtonFunc = &amp;ButtonFunc; }   If anyone has any advice on how I can properly send this function so that I can use it later. How is Starkiller Base's beam visible from Takodana in The Force Awakens? On Takodana,      the main characters and various bar patrons can see the planet Hosnian Prime being destroyed by Starkiller Base with their (respective) naked eyes. How did they see this? Is the Hosnian system close enough to see? If it's not very close and they could just see the explosion, how did the light from it reach them so quickly? I'm using Bash on both client and server. When running a command over SSH:   ssh &lt;host&gt; 'declare' gives a list of shell variables. ssh &lt;host&gt; 'mount' gives a list of mountpoints.   However, declare is a Bash builtin, while mount is an external command. How does SSH know which to run if there is a shell builtin and an external command with the same name on the server? I encountered this particular combinatorial identity :$$\begin{align}&amp;1\dbinom{n-1}{r-1}+2\dbinom{n-2}{r-1}+\cdots+(n+1-r)\dbinom{r-1}{r-1}\\=&amp;\dbinom{n}{r}+\dbinom{n-1}{r}+\cdots+\dbinom{r}{r}\\=&amp; \dbinom{n+1}{r+1}\end{align}$$How does one figure it out? I have a laptop with a full keyboard (it has numpad), but the laptop is not that big, and because of that the keys are relatively small, which means I am constantly finding myself pressing keys accidentally on the numpad part.  Is there a way to disable specific keys that I simply don't want? Any way to open windows from the windows bar using a shortcut? for example to open the first window on the left Ctrl+1, to open the second window on the left Ctrl+2.  Im using xfce4 at this moment, but if under xfce4 is not possible, is there any other desktop environment that permits this?  Since I have several windows open for the same application, I not searching for sortcuts related to the application but as I say below, to the window.