Prove that $\operatorname{lcm}(a,b,c)=\frac{abc \operatorname{gcd}(a,b,c)} {\operatorname{gcd}(a,b)\operatorname{gcd}(b,c)\operatorname{gcd}(c,a)}$
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
Can I make an ender portal on creative? I've updated Minecraft PE, and in the update notes it states that they've added the End. But when I made a new creative world and built a portal, it didn't work.  I've been looking online at tutorials, but cannot get the portal to open. So how do you create an Ender Portal? Windows keeps making these random "device connect" and "device disconnect" sounds Throughout the day I notice that my computer makes apparently random device-connect and/or device-disconnect ("boink") sounds.    I suppose it is the same sound you hear when connecting or disconnecting a USB device such as a thumb drive.  I've noticed that this happens on each of three computers I work with at home, my wife's computer, and my machine at work.  It happens without any user action at all - i.e. I'll be just sitting there (hands off my mouse and keyboard), and the computer will make the sound.  There is no visual queue or anything.  Just the sound.  I have sometimes gone in pursuit of the sound - running virus scans, examining event logs and such, and observing task manager - but have never had any luck tracking this thing down, but have not had any luck.  I've been noticing this since Windows Vista and now the sounds have followed me through to Windows 7.   Surely someone else out there must be experiencing this and can explain what is happening. Ship an application with a database What's a word for a positive kind of "envy" without the sense of resentment? Imagine your college buddy is now running a multi-billion dollar company, while you're still stuck at the same white-collar day job 5 years after graduation. You chat with him and want to express the idea that you're happy for him and fancy having his lifestyle--something like "I wish I could buy a yacht and cruise around the world like you do; I'm glad you're doing really well!"  Basically, it's the feeling of envy when you take out the resentment from it. Is there a word for it?   (I thought about "admire", but found it too strong and broad) While accepting an offer to grad school, one is basically entering into a lasting relationship with one's adviser - most likely, someone whom the applicant has never met before, and the only exposure has been through the potential adviser's website/publications. It is in the interest of both parties to ensure (to the greatest possible extent) that there are no personal/professional traits of either that hamper the formation of a pleasant working relationship - no-one would want to go through the ordeal of having to change advisers midway!  While the faculty has a chance to have a good look at the applicant's profile as well as his motivations (through his grades and SOP), the applicant doesn't have a similar opportunity. So, I'm interested to know what parameters can be used to gauge a potential fit. I've thought of the following:   Past students:  Did anyone ever drop out/change advisers midway, and if so, for what reasons? These would be a bit hard to find though, as I don't expect the faculty concerned would list them on their website. It would be great if anyone could let me know how to find out the list of incoming students to a department for any year. Publication rate, taking into account the venues where they were accepted. Time taken to graduate - though I accept this is more dependent on the student, a median figure should be telling ... What they did post Ph.D. - did anyone get tenure if they went into academia, or is almost everyone unable to break out of being a post-doc?  Tenure status: I'm a bit unsure about this, so wanted the community's opinions about it. Just so that I'm clear, I'm only trying to calibrate the applicant's expectations about the working style of his potential adviser - and hence need to know to what extent are the following "typical" assumptions valid.  Tenured professor  A full professor is more likely to get grant funding, hence less time spent on TAship - but could also mean less time/effort spent on interactions with students (either being busy with other projects/talks, or due to more commitments to family at that age).  Tenure-track faculty (Assistant profs)  More likely to be young and energetic, and could translate to more time spent on one-to-one discussions with grad students - but funding may prove to be an issue, and may have to be on TA for a longer period.   What other factors would be relevant in this matter, and to what extent am I correct/incorrect in either the factors considered, or for undertaking this exercise at all? setuid root does not work Objective : Run a program as root (C++ binary). The same as :   And :   ./a.out output:  E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? psurana  //output for "whoami" Look below for the code.   ls -l output:  -rwsrwxr-x 1 root    root    46136 Jun  7 20:13 a.out  The Code :   #include &lt;string&gt; #include &lt;stdlib.h&gt; int main(int argc, char *argv[]){         std::string input = "apt-get install " + std::string(argv[1]);         system(input.c_str());         system("whoami");         return 0; }   Details: : compiled the program and then did chown root:root a.out &amp;&amp; chmod u+s a.out. Please look above for ls -l output.  I still do not get the root privileges and the output for system("whoami") in the code is my own username on the machine.  Reading the two linked questions did not yield me anywhere. :(. both the creator and the owner of the file are root. The setuid bit is set, so it should work. The filesystem is not external either, it is my own machine. How can I make this work? Attempt to de-reference a null object: Trigger There were custom validation error(s) encountered while saving the affected record(s). The first validation error encountered was:      Apex trigger updatequotestatus caused an unexpected exception, contact your administrator: updatequotestatus: execution of AfterInsert caused by: System.NullPointerException: Attempt to de-reference a null object: Trigger.updatequotestatus line 5, column 1.   Error Occured at Line:     if((t.what.getsobjecttype() == quote__c.sobjecttype) &amp;&amp; (t.subject.substring(0,5) == 'Email')  trigger updatequotestatus on task (after insert, after update){     Set&lt;Id&gt; quoteIds = new Set&lt;Id&gt;();     List&lt;quote__c&gt; quotes = new List&lt;quote__c&gt;();      for(task t:trigger.new){         if(t.whatId!=null){             if((t.what.getsobjecttype() == quote__c.sobjecttype) &amp;&amp; (t.subject.substring(0,5) == 'Email')){                 quoteIds.add(t.whatId);             }         }     }      for(quote__c q:[select StageName__c from quote__c where Id IN : quoteIds]){         quote__c qt = new quote__c();         qt.Id = q.Id;         qt.StageName__c = 'Proposal Sent';         quotes.add(qt);     }      if(quotes.size()&gt;0){         update quotes;     } } How to set a maximum execution time for a mysql query? I would like to set a maximum execution time for sql queries like set_time_limit() in php. How can I do ? The space $c_0$ of sequences that converge to 0 is not reflexive Studying for CISSP these choices seemed limited:     What is the advantage of digital signatures over message authentication codes?         Digital Signature provides integrity verification while message authentication code does not   Digital Signature provides confidentiality while message authentication code does not   Digital Signatures provide authenticity while message authentication code does not   Digital Signatures works faster than message authentication codes      Using the following chart as a reference, I'm leaning towards #2, but none of the choices really fit properly…  Cryptographic primitive | Hash |    MAC    | Digital Security Goal           |      |           | signature ------------------------+------+-----------+------------- Integrity               |  Yes |    Yes    |   Yes Authentication          |  No  |    Yes    |   Yes Non-repudiation         |  No  |    No     |   Yes ------------------------+------+-----------+------------- Kind of keys            | none | symmetric | asymmetric                         |      |    keys   |    keys   Hopefully an expert here can clarify. Using CLI, how do I change the user's profile picture? A similar task for changing the desktop background, can be achieved using the following script:   FILE="/backgrounds/background.png" gsettings set org.gnome.desktop.background picture-uri "$FILE"   How would I achieve the same result, but with the user's avatar/profile picture? I have currently a strange problem on debian (wheezy/amd64).  I have created a chroot to install a server (i can't give any more detail about it, sorry). Let's call its path /chr_path/. To make things easy, I have initialized this chroot with a debootstrap (also wheezy/amd64).  All seemed to work well inside the chroot but when I started the installer script of my server I got : zsh: Not found /some_path/perl (the installer includes a perl binary for some reasons)  Naturally, I checked the /some_path/ location and I found the "perl" binary. file in chroot environment returns :  /some_path/perl ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.2.5, not stripped   The file exists, seems ok, has correct rights. I can use file, ls, vim on it but as soon as I try to execute it - ./perl for example - I get : zsh: Not found ./perl.  This situation is quite understandable for me. Moreover :   I can execute other basic binaries (/bin/ls,...) in the chroot without getting errors I have the same problems for other binaries that came with the project When I try to execute the binary from the main root (/chr_path/some_path/perl), it works. I have tried to put one of the binaries with a copy of my ls. I checked that the access rights were the same but this didn't change anything (one was working, and the other wasn't) How to distinguish gift from payment for the service? If somebody gives me reasonable advise or share important to me information.   Being attentive I would like to make a little gift or give some little (&lt;100$) amount of money (cash/wire/online) for that   How it would be classified by IRS?   Which obligations originate with this matter for me and my party?  How to do this in a most comfortable way to my party? Does one need a visa to transfer between two airports during a transit through the Schengen area? I am an Indian citizen travelling from New York to Delhi with a layover in Paris where I need to transfer between Paris Orly Airport (ORY) and Paris Charles de Gaulle Airport (CDG).  Do I need to have a visa to make this transfer?  I didn't notice that while booking the ticket. Does the speed of light vary in non-inertial frames? The speed of light is the same in all inertial frames.  Does it change from a non-inertial frame to another? Can it be zero?  If it is not constant in non-inertial frames, is it still bounded from above? How can I remap a keyboard key? One of my laptop's keys has fallen off. Is there any way I can remap another key to serve as that key?  I'll 'sacrifice' the other key because I never use it. Very good linear algebra book. I plan to self-study linear algebra this summer. I am sorta already familiar with vectors, vector spaces and subspaces and I am really interested in everything about matrices (diagonalization, ...), linear maps and their matrix representation and eigenvectors and eigenvalues. I am looking for a book that handles every of the aforementioned topics in details. I also want to build a solid basis of the mathematical way of thinking to get ready to an exciting abstract algebra next semester, so my main aim is to work on proofs for somehow hard problems. I got Lang's "Intro. to Linear Algebra" and it is too easy, superficial.  Can you advise me a good book for all of the above? Please take into consideration that it is for self-study, so that it' gotta work on its own. Thanks. I think my device got a malware. A lock screen with ads sometimes appear, and I must swipe an area at the bottom of the screen to open the phone. I am in Eastern Europe, some ads are in Slavic languages, and they are seemingly related to travel.    Image resized. Click to view the full image  I have seen ads for Lot Air (Polish carrier). I recently went to their site.  Considering my recent surfing activity and the nature of the ads, I guess the malware is connected to airlines active in Eastern Europe.  The lock screen also promotes the app "DU Quick Charger" by claiming it has recharged the phone extra fast during screen off. (!?) It also shows battery level. I have never installed DU Quick Charger. I doubt DU Quick Charger is installed on the phone.  The problem started after installing Ryanair app. The problem is maybe, but not surely, related to this. Uninstalling Ryanair and restarting the phone doesn't remove the occasional appearance of this lock screen. After a while the situation has changed for the worse, now this lock screen appears after EVERY screen off.  I have always used Avast. I am not rooted and only install via Google Play.  What is this? And how do I remove it? How can I flush the output of the print function? How do I force Python's print function to output to the screen? Fastest Gun in the West Problem I feel like there's a problem with Stack Overflow, as the number of people prowling it increases.  Each question's answers are sorted by descending score and then by descending time of posting. This means that if a person sits down and answers a question in a long, thorough way, going through every nook and cranny, once they post their answer, it will already be one of about seven different ones, some of which have already been upvoted. This wouldn't be a problem if those answers were as thorough as the one this guy's posting, but they usually aren't. Some of them are downright wrong, some aren't even answers to the question asked because their poster didn't bother to read the question all the way through.  This causes a problem I like to call Stack Overflow's Fastest Gun in the West Problem. I've come to a point where I'd rather just send a short, simple, correct explanation, than to go and do some proper research, write a whole blog post about it or even make sure the code I post even compiles, just so it will be noticed, as opposed to the incorrect ones.  I'm sure I'm not the only one doing this and that it despairs many people from even trying to answer questions.  I've long ago learned to try to always raise a problem with a solution in hand, rather than just say "This is a problem, handle it," so my question, after this long tirade, is:     How do you think this can be changed? What would you change in Stack Overflow to make this problem go away without hurting the site?   I promise to vote on answers I like, even if it takes you a long while to post them. :)