Suppose $f(x)$ is a polynomial with integer coefficient. If there exist $a$, $b$, $c$, $d$ such that $f(a)=f(b)=f(c)=f(d)=5$ then there does not exist $k$ such that $f(k)=8$. Prove.  We consider $Q(x)= f(x)-5$. Then $Q(x)$ has 4 distinct roots. According to the problem given, $Q(k)=3$. Hence $(k-a)(k-b)(k-c)(k-d)r(k)=3$. Hence we can not find any contradiction!
There is a polynomial $f$ of integer coefficients such that $\deg(f) \geq 4$. Let's assume that there are four integers $a,b,c,d$ for which $f(a)=f(b)=f(c)=f(d)=5$. Prove that there is no integer $k$ for which $f(k)=8$ - I'd like to have a full explanation to solution.
How do I run a batch file from my Java Application? In my Java application, I want to run a batch file that calls "scons -Q implicit-deps-changed build\file_load_type export\file_load_type"  It seems that I can't even get my batch file to execute. I'm out of ideas.   This is what I have in Java:  Runtime.    getRuntime().    exec("build.bat", null, new File("."));   Previously, I had a Python Sconscript file that I wanted to run but since that didn't work I decided I would call the script via a batch file but that method has not been successful as of yet. Why can't my subclass access a protected variable of its superclass, when it's in a different package? Find all Facebook comments on external websites Is there any way to find all comments on external websites connected with a Facebook account? Let's say I want to find all my Facebook activity on external pages based on profile URL; is there any way to do this? Restore console session after remote desktop disconnects? Is it possible (through group policy, etc) to automatically restore the console session to a Windows 8.1 PC after a remote desktop session disconnects?  I'm aware that you can run the command "tscon 1 /dest:console" during the RDP session to disconnect yourself and reconnect the console session, but is it possible to have this happen automatically? My document should be letterpaper and my attachments should be a4paper. I had high hopes for the \newgeometry command from the geometry package, but the documentation says      \newgeometry is almost similar to   \geometry except that \newgeometry   disables all the options specified in   the preamble and skips the   papersize-related options: landscape,   portrait and paper size options (such   as papersize, paper=a4paper and so   forth).   Any help is appreciated! How is the amplitude of light related to number of photons? If you increase the number of photons leaving a light source you increase the brightness/intensity, so it could be said that intensity is directly proportional to number of photons. However intensity is directly proportional to amplitude squared, so this leads me to wonder that if you increase the amplitude of a light wave, are you just creating more photons rather than affecting each individual photon in some way? Why does space expansion not expand matter? I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me. How to check if a service is running on Android? How do I check if a background service is running?  I want an Android activity that toggles the state of the service -- it lets me turn it on if it is off and off if it is on. Why $∀x(P(x)→Q)$ is equivalent to $∃xP(x)→Q$ Given $x$ occurs free in $P$. If $x$ does not occur free in $Q$, then $∀x(P(x)→Q)$ is semantically equivalent with $∃xP(x)→Q$. How to understand this statement. And also, need an example to show that the formula will not necessarily be equivalent if $x$ does occur free in $Q$.  I guess what struggles me is I'm not quite understand what does "free" mean in this case. But it would be better to have answer for the above question. Can I nohup/screen an already-started process? Have iOS apps. Can I use them on my Mac Mini? I bought many iOS Apps on various iPads and iPod touchs. This Wednesday I will have my first Mac, a Mac Mini, so my question is: Will I be able to download these Apps without any charge, if they are available on Mac Store?  I ask this because I have been watching some videos and have seen GarageBand on the Mac but I don't know if it's the same App. I know that the App Store and Mac Store are different, but, like some Apps on AppStore have a plus symbol on their icons corners saying these Apps can be run on iPad, iPod touch and iPhone I wonder whether there will be some Apps for both iOS and the Mac.  Also, I don't know if GarageBand was released on Mac before iOS devices. Show that $3p^2=q^2$ implies $3|p$ and $3|q$ This is a problem from "" (specifically, exercise set 2 #9), which is one of my math texts. Please note that this isn't homework, but I would still appreciate hints rather than a complete answer.  The problem reads as follows:     If 3p2 = q2, where $p,q \in \mathbb{Z}$, show that 3 is a common divisor of p and q.   I am able to show that 3 divides q, simply by rearranging for p2 and showing that  $$p^2 \in \mathbb{Z} \Rightarrow q^2/3 \in \mathbb{Z} \Rightarrow 3|q$$  However, I'm not sure how to show that 3 divides p.    Edit:  Moron left a comment below in which I was prompted to apply the solution to this question as a proof of $\sqrt{3}$'s irrationality. Here's what I came up with...  [incorrect solution...]  ...is this correct?  Edit:  The correct solution is provided in the comments below by Bill Dubuque. I want to create an image like below, so a balloon with text on it.     I have been googling for ideas (text, sphere, ....) and came on  earlier question. So I tried Shrinkwrap and Cast modifier.   Here is the situation before applying the modifiers.    This was after trying Shrinkwrap    And this after Cast modifier.    For me it does not look like it is going to work with one of these modifiers.  Question How to create the image of a balloon with text on it ? With one of these modifiers or should I try a complete other approach ?? How to do this ? Javascript custom button stopped working, Synchronous XMLHttpRequest is deprecated We have a custom javascript button on the quotes object in our org that has been working for several months that someone has noticed today is not working.    I'm not sure if there was an update that broke it or what day exactly it stopped working.  I'm hoping someone has an idea of where I can even begin to look.   Here's the code:   javascript:location.href= 'mailto:emailaddress@ourdomain.com?SUBJECT='+ escape("{!Quote.Name}")+' - '+ escape("{!Quote.Contact_s_Account__c}") + '&amp;BODY=Please convert ' + escape(location.href)+ ' into a proposal and send it to the email address on the quote.  Thanks!';   Using developer tools in chrome, I see this error after I click the javascript button:   presence: onFailure in event parser ={"status":-5,"statusText":""}page load happens value=true           umps1w4.salesforce.com/umps/UMPSWidget_184/js/dist/umps-min.js?cflag=184.36:14 presence: onFailure in event parser ={"status":-5,"statusText":""}page load happens value=true   I changed my code to something simple:   javascript:location.href= 'mailto:emailaddress@ourdomain.com?SUBJECT='hello'    and got this error in the developer tools in chrome:   Synchronous XMLHttpRequest on the main thread is deprecated because of its detrimental effects to the end user's experience. For more help, check http://xhr.spec.whatwg.org/.   This lead me to the conclusion that I'm having XSS issues.  I do remember a SF update not too long about about protecting against XSS issues.  I guess I'll have to figure out a different way to implement this functionality. The Many Memes of Meta Catchphrases and concepts that spread from person to person are known as [memes], which, courtesy the Internet, can now explode across the Earth like a highly contagious virus (hence &quot;going viral&quot;). As with their real-life counterparts, some infectious diseases are global (pandemic), while others are endemic to specific regions. Stack Overflow, and now even more predominantly Meta Stack Exchange, have seen more than their fair share of these pathological social constructs spread through the user base. They are now ingrained units of our collective culture as SOpedians (a term which I hate, by the way). Just as travelers' immune systems can be assaulted by new diseases in new places, new users are increasingly likely to be miffed by an ingrained meme and left sitting scratching their heads. I therefore propose that this space be used to document the memes endemic to Stack Exchange's culture. Each meme should be listed in a separate answer and I hope that we as a community will be able to provide greater context to each one. Please actually explain each meme in a way understandable to those not already in the know. Especially considering that a lot of these memes aren't really understandable to newer users who weren't around in the early years of the network, or are based on system features that no longer exist.  On other Stack Exchange sites          [memes]: In episode 10 of Full Metal Alchemist: Brotherhood, during the events in the Research Lab 5, Edward Elric is severely hurt. Later in the hospital, he writes down everything he had come to know, and he discusses with Alphonse, Hughes, and Armstrong about what to do with the information to continue the investigation.  At this point, King Bradley arrives with lemon into the room. He finds out what they are doing but acts very calm and chilled out and allows them to continue investigation while being careful.  Why did he not get Hughes and Armstrong killed at that point? Or at least tell them to not investigate at all? How to stop people from using my domain to send spam? I receive Mailer Daemon messages saying certain emails fail. My domain is itaccess.org which is administered by Google apps. Is there any way I can identify who is sending emails from my domain, and how they are doing it without me creating an account for them?  Delivered-To: 7e949ba@itaccess.org Received: by 10.142.152.34 with SMTP id z34csp12042wfd;         Wed, 8 Aug 2012 07:12:46 -0700 (PDT) Received: by 10.152.112.34 with SMTP id in2mr18229790lab.6.1344435165782;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Return-Path: &lt;whao@www20.aname.net&gt; Received: from smtp-gw.fsdata.se (smtp-gw.fsdata.se. [195.35.82.145])         by mx.google.com with ESMTP id b9si24888989lbg.77.2012.08.08.07.12.44;         Wed, 08 Aug 2012 07:12:45 -0700 (PDT) Received-SPF: neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) client-ip=195.35.82.145; Authentication-Results: mx.google.com; spf=neutral (google.com: 195.35.82.145 is neither permitted nor denied by best guess record for domain of whao@www20.aname.net) smtp.mail=whao@www20.aname.net Received: from www20.aname.net (www20.aname.net [89.221.250.20])     by smtp-gw.fsdata.se (8.14.3/8.13.8) with ESMTP id q78EChia020085     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:43 +0200 Received: from www20.aname.net (localhost [127.0.0.1])     by www20.aname.net (8.14.3/8.14.3) with ESMTP id q78ECgQ1013882     for &lt;7E949BA@itaccess.org&gt;; Wed, 8 Aug 2012 16:12:42 +0200 Received: (from whao@localhost)     by www20.aname.net (8.14.3/8.12.0/Submit) id q78ECgKn013879;     Wed, 8 Aug 2012 16:12:42 +0200 Date: Wed, 8 Aug 2012 16:12:42 +0200 Message-Id: &lt;201208081412.q78ECgKn013879@www20.aname.net&gt; To: 7E949BA@itaccess.org References: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; In-Reply-To: &lt;20120808171231.CAC5128A79D815BC08430@USER-PC&gt; X-Loop: whao@whao.se From: MAILER-DAEMON@whao.se Subject: whao.se:  kontot avstängt - account closed X-FS-SpamAssassinScore: 1.8 X-FS-SpamAssassinRules: ALL_TRUSTED,DCC_CHECK,FRT_CONTACT,SUBJECT_NEEDS_ENCODING      Detta är ett automatiskt svar från F S Data - http://www.fsdata.se      Kontot för domänen whao.se är tillsvidare avstängt.     För mer information, kontakta info@fsdata.se      Mvh,     /F S Data      -----    This is an automatic reply from F S Data - http://www.fsdata.se    The domain account "whao.se" is closed.   For further information, please contact info@fsdata.se    Best regards,   /F S Data Where to place my local website starting with the 2.4.7 version of apache2? Sudo doesn't work on Aliases I have added alias ll='ls -la' in /etc/bash.bashrc but sudo ll is not working. Is there a way to "source" bash.bashrc? In a related post, another user suggesting creating an alias for sudo with a space after it. Eg. alias sudo='sudo ' but there wasn't any context to this answer. Should I add this to my bashrc? Seems hackish.  What is the correct method for adding an alias for my sudo one-off commands? Does MariaDB or MySQL implement the VALUES (expression) table value constructor?