Prove that it is impossible to find any positive integers a, b, c such that $(2a+b)(2b+a) = 2^c$
Prove that the expression cannot be a power of 2
Suppose the proper length of a train is longer than that of a bridge, and the bridge can't bear the total weight of the train but can bear it partially. As the train goes very fast, it becomes shorter than the bridge and it can be entirely on the bridge. As a result, the bridge will collapse. However, in the train's frame, the train is even longer than the bridge, and it is only partially on the bridge; so the bridge will not collapse. What is the solution to this paradox? I'm using an HP laptop running Windows 7 Home Edition.  The moment I reach the login screen the computer automatically types "ppppppppp" in the password place, luckily I have fingerprint login to counter that.  The moment I login, it keeps acting as if I'm typing 'p' repeatedly. I tried removing the button and cleaning under it but it was no use. I've tried restarting, uninstalling the keyboard driver, but it was no use.  I can't go to Control Panel because the moment I get there, it starts typing "pppppp" in the search field and I'm unable to find anything.  I'm typing this from my phone because going anywhere on my laptop seems impossible. VS Code Setup - Create project with manifest error When I try to create project with manifest it is giving me this error:    Starting SFDX: Create Project  12:39:56.757 sfdx force:project:create --projectname Dev --outputdir c:\ --template standard --manifest { AssertionError [ERR_ASSERTION]: Trying to copy from a source that does not exist: C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\lib\templates\project\standard\ScratchDef.json     at EditionInterface.exports.copy (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\mem-fs-editor\lib\actions\copy.js:49:3)     at EditionInterface.module.exports [as copyTpl] (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\mem-fs-editor\lib\actions\copy-tpl.js:29:8)     at ProjectGenerator.writing (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\lib\generators\projectGenerator.js:57:17)     at Object.&lt;anonymous&gt; (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\yeoman-generator\lib\index.js:427:27)     at C:\Program Files (x86)\Salesforce CLI\client\node_modules\run-async\index.js:25:25     at new Promise (&lt;anonymous&gt;)     at C:\Program Files (x86)\Salesforce CLI\client\node_modules\run-async\index.js:24:19     at self.env.runLoop.add.completed (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\yeoman-generator\lib\index.js:428:13)     at runCallback (timers.js:705:18)     at tryOnImmediate (timers.js:676:5)   generatedMessage: false,   name: 'AssertionError [ERR_ASSERTION]',   code: 'ERR_ASSERTION',   actual: false,   expected: true,   operator: '==' } { AssertionError [ERR_ASSERTION]: Trying to copy from a source that does not exist: C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\lib\templates\project\standard\ScratchDef.json     at EditionInterface.exports.copy (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\mem-fs-editor\lib\actions\copy.js:49:3)     at EditionInterface.module.exports [as copyTpl] (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\mem-fs-editor\lib\actions\copy-tpl.js:29:8)     at ProjectGenerator.writing (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\lib\generators\projectGenerator.js:57:17)     at Object.&lt;anonymous&gt; (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\yeoman-generator\lib\index.js:427:27)     at C:\Program Files (x86)\Salesforce CLI\client\node_modules\run-async\index.js:25:25     at new Promise (&lt;anonymous&gt;)     at C:\Program Files (x86)\Salesforce CLI\client\node_modules\run-async\index.js:24:19     at self.env.runLoop.add.completed (C:\Program Files (x86)\Salesforce CLI\client\node_modules\salesforcedx-templates\node_modules\yeoman-generator\lib\index.js:428:13)     at runCallback (timers.js:705:18)     at tryOnImmediate (timers.js:676:5)   generatedMessage: false,   name: 'AssertionError [ERR_ASSERTION]',   code: 'ERR_ASSERTION',   actual: false,   expected: true,   operator: '==' } 12:40:03.206 sfdx force:project:create --projectname Dev --outputdir c:\ --template standard --manifest  ended with exit code 0   Can you please let me know what I am missing:   I have:   installed vs code, salesforce extension pack, salesforce cli, set the environment variable for my user, there is jdk installed (I have not set the path for it, not sure if it is required?)    What I am missing?   Thanks in Advance!! How can I use docker without sudo? On Docker's documentation pages, all example commands are shown without sudo, like this one:  docker ps   On Ubuntu, the binary is called docker.io. It also does not work without sudo:  sudo docker.io ps   How can I configure Docker so that I don't need to prefix every Docker command with sudo? OK, I've been having weird problems for the last 1/2 hour trying to  on StackOverflow, and I keep getting this result (on Firefox 3.6)     The connection was reset      The connection to the server was reset while the page was loading.         The site could be temporarily unavailable or too busy. Try again in a few        moments.   If you are unable to load any pages, check your computer's network        connection.   If your computer or network is protected by a firewall or proxy, make sure        that Firefox is permitted to access the Web.      The problem seems to occur when I try to post some code with 'd--- table' in it, where 'd---' is replaced by the word drop.  I cannot post the following 3 lines, in either SO or this site, if they include the well-known SQL statements DROP.  stat.executeUpdate('d--- table if exists people;'); stat.executeUpdate('create table people (name, occupation);'); prep = conn.prepareStatement(...     'insert into people values (?, ?);');   test again:  'dro* table' 'drop ball' drop the table drop fable drop    t*ble droptable   drop a table  The evil words for me are "drop" and "table"... how come you guys can post? :(  edit: Could someone please suggest another online site that is not stackoverflow that is a quick way to try out a POST request of a text field?  UPDATE: Never mind. I don't know what the answer is, but the same problem occurs on Google's website. So it's not stackoverflow. Now to go to my IT Dept... Visual Studio C# statement collapsing When editing really long code blocks (which should definitely be refactored anyway, but that's beyond the scope of this question), I often long for the ability to collapse statement blocks like one can collapse function blocks.  That is to say, it would be great if the minus icon appeared on the code outline for everything enclosed in braces.  It seems to appear for functions, classes, regions, namespaces, usings, but not for conditional or iterative blocks.  It would be fantastic if I could collapse things like ifs, switches, foreaches, that kind of thing!  Googling into that a bit, I discovered that apparently C++ outlining in VS allows this but C# outlining in VS does not.  I don't really get why.  Even notepad++ will so these collapses if I select the C# formatting, so I don't get why Visual Studio doesn't.  Does anyone know of a VS2008 add-in that will enable this behavior?  Or some sort of hidden setting for it?  Edited to add: inserting regions is of course an option and it did already occur to me, but quite frankly, I shouldn't have to wrap things in a region that are already wrapped in braces... if I was going to edit the existing code, I would just refactor it to have better separation of concern anyway. ("wrapping" with new methods instead of regions ;) Word that describes being "patriotic" for something that is not a country? I'm looking for a word that is similar to patriotic but does not relate to one's country (or state).  For what it's worth, I'm specifically referring to "overly patriotic" in a negative sense, to describe someone who has a overly sentimental/cultural or otherwise less-than-rational attachment or devotion to something and makes it part of their very identity. A common example might be an extremely zealous football fan. I am trying to find all 1- or 2- dimensional Lie Algebras "a" up to isomorphism. This is what I have so far:  If a is 1-dimensional, then every vector (and therefore every tangent vector field) is of the form $cX$. Then , by anti-symmetry, and bilinearity:  $$[X,cX]=c[X,X]= -c[X,X]==0$$  I think this forces a unique Lie algebra because Lie algebra isomorphisms preserve the bracket.  I also know Reals $\mathbb{R}$ are the only 1-dimensional Lie group, so its Lie algebra ($\mathbb{R}$ also) is also 1-dimensional. How can I show that every other 1-dimensional algebra is isomorphic to this one? Do I use preservation of bracket?  For 2 dimensions, I am trying to use the fact that the dimension of the Lie algebra g of a group $G$ is the same as the dimension of the ambient group/manifold $G$. I know that all surfaces (i.e., groups of dimension 2) can be classified as products of spheres and Tori, and I think the only 2-dimensional Lie group is $S^1\times S^1$, but I am not sure every Lie algebra can be realized as the Lie algebra of a Lie group ( I think this is true in the finite-dimensional case, but I am not sure).  I know there is a result out there that I cannot yet prove that all 1- and  2-dimensional Lie algebras are isomorphic to Lie subalgebras of $GL(2,\mathbb{R})$ (using matrix multiplication, of course); would someone suggest how to show this last? Thanks. Redirect non-www requests to www on Amazon Route 53 I want to redirect all requests from example.com to www.example.com.   Preferably, this should happen at DNS level. I tried using PTR records, but that simply fails, returning a 404.  wwww.example.com is an ALIAS for an Elastic Load Balancer.  What’s the simplest way to achieve this? setting up subdomain on ubuntu server Upgrading from Yosemite to El Capitan, but not Sierra Is it legal to add your publications to ResearchGate? I recently created a profile on . And to add your publications list it requires you to upload the paper. Is it legal to upload published journal articles on public servers, where everyone can download it for free? Is it theoretically possible that every person in this village has a different jar of coins? A village has about $1$ million residents. Suppose each resident has a jar with $100$ coins in it.Two jars are considered to be “equivalent” if they have the same number of 10c, 20c, 50c, $\$$1 and $\$$2 coins in them. How many different (i.e. nonequivalent) jars of coins exist? Is it theoretically possible that every person in this village has a different jar of coins?  I understood that if we have $k_1$ 10 coins in the jar where $k_1$ is between $0$ and $100$ inclusive, then there are $100-k_1$ coins of other denominations in the jar. Likewise, we also have $k_2$ 20c coins in the jar where $k_2$ is between $0$ and $100$ inclusive, so the combined number of 50c, $\$$1, and $\$$2 coins in the jar is $100-k_1-k_2$. And we always have some $k_1, k_2, k_3, k_4, k_5$, let's say, so that the sum of those $k$'s is $100$.  I got stuck since I don't know how to 'compare' the number of coins in jars for different residents. Javascript mechanism to autoscroll to the bottom of a growing page? How to disable battery charging? From the pmset man page:     POWER SOURCE ARGUMENTS      -g with a 'batt' or 'ps' argument will show the state of all attached power sources.      […] Certain Apple battery calibration tools may temporarily disable   battery charging, even though your Apple portable is plugged into AC   power.      Such tools will never surprise you with this behavior; you will know   it's happening. This state will be reflected in an additional line of   output to 'batt' or 'ps' readings, including the pid of the app   inducing this behavior.       'ChargeInhibit':    1432    So, does any piece of publicly available software exist to force the battery not to charge? List questions: Community Wiki? Need to understand why my Schengen visa was refused Logic gate - What will be the second input of each gate? Full:    Cropped   :    In the second image (cropped) which is the same as the first (full) image... why the 1st Gate outputs "0"? I have been trying but its not working.  but if i try   &lt;?php echo do_shortcode("[mimo]"); ?&gt; &lt;?php echo do_shortcode("[mibaby]"); ?&gt;   it will work fine.  But to apply it in post content using [mimo] [mibaby]  it won't work.  Here is the Functions i am using...  function wpb_custom_new_menuw() {   remove_filter( 'the_content', 'wpautop' ); } add_shortcode('mibaby', 'wpb_custom_new_menuw');    function wpb_custom_new_menu() {   remove_filter( 'the_excerpt', 'wpautop' ); } add_shortcode('mimo', 'wpb_custom_new_menu'); How can I get my graphics card to be recognized in System Info?