How do I prove that the connected undirected graph having 10 nodes and 10 edges contains a cycle.
How to prove this question? If a graph with $n$ vertices and $n$ edges it must contain a cycle?
Address is invalid on local machine [on windows 8 only] $k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$ I would like to prove the following equality: $$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}$$if $\gcd(l,k)=1$. What methods can I use? Thank you for your help. In Book 1, Artemis et al escaped from the time stop by drugging themselves to sleep.  In the same time stop, Julius Root "accidentally" plugged Briar Cudgeon with a tranquilizer dart.  Cudgeon fell asleep, but did not disappear from the time stop.  Why not? Can I travel within the Schengen area without a passport if I have my residency permit card? I am currently located in the Netherlands and have lived here for 4 years. I have a working visa for the Netherlands and would like to go on vacation to another country in Europe. I however do currently not have my passport as i sent it to an embassy for a visa application. Will I still be able to travel inside of Europe without a passport if I have my residency ID?  I have a resident permit, not a true Dutch ID. And I own a passport that is currently in transit.  I have called with the KLM and the service employee's conclusion was that I do need to carry my passport with me when i am going to fly, so it seems all I can do is wait and hope my passport is returned to me in the next few days as the amsterdam US consulate (who currently holds my passport) is incredibly difficult to contact for urgent matters. I have a scene below where I am wanting to get an HDRI image to come in through the windows and light the scene in the window areas and have a god ray like effect.  I want to do this with a volumetric effect and have the HDRI lighting create throw patterns in the scene.  Is this possible?  To have volumetric lighting where the HDRI creates throw patterns?  Thanks for the help How to find and return a duplicate value in array why is my screen black after rdp connection? After connecting from my home via remote desktop, both my screens are black when I arrive at work. The only thing I can see is a mouse pointer on one of the screens. I then seem to have only two choices: rebooting or working from a remote desktop connection, which works fine.  It did happen every time I tried last week.  However, I did the same from my laptop in a meeting room today, and I didn't have any problem. How do you read C declarations? I have heard of some methods, but none of them have stuck. Personally I try to avoid complex types in C and try to break them into component typedef.  I'm now faced with maintaining some legacy code from a so called 'three star programmer', and I'm having a hard time reading some of the ***code[][].  How do you read complex C declarations? Stack Exchange API too many requests from this IP address PhD Student : Publish Paper with Wife? Changing the size of the mouse pointer in Ubuntu MATE 18.04 does not work I have Ubuntu 18.04 with the gnome-desktop  and parallel the Ubuntu MATE desktop installed. While I can easily change the size of the mouse pointer (DMZ-White) in the Gnome3 desktop , this does not work on the MATE desktop. I use for this the dconf-editor.  Maybe someone knows a solution?  Thanks a lot. Is there any actual written dialog for the astromech droids? When R2-D2 and BB-8 converse in The Force Awakens for example, is there any written record of what the two characters were saying to each other?  I mean actual dialog, if it exists, and not something like ”BB-8 beeps excitedly”. Is it possible to find all php files within a certain directory that have been modified on a certain date  I'm using   find /var/www/html/dir/ -mtime -28 | grep '\.php'    to get files modified within the last 28 days, but I only need files that have been modified on the following date: 2011-02-08 Allow converting comments to answers Allow converting comments to answers, so they can become accepted answers.  I asked a question. Someone commented on it, and it was an awesome comment that fully answered the question. As the original questioner, I would like to convert that comment to an answer in order to accept it.  Or, if you prefer, I would be okay with being able to simply mark the comment as accepted. Matrices $B$ that commute with every matrix commuting with $A$ The output from uname:  root@debian:~ # uname -a Linux 5asnb 2.6.32-5-amd64 #1 SMP Mon Jun 13 05:49:32 UTC 2011 x86_64 GNU/Linux   However the /sbin/init executable shows up as 32-bit:  root@debian:~ # file /sbin/init /sbin/init: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), dynamically linked (uses shared libs), for GNU/Linux 2.6.18, stripped   Other aspects of the system seem to contradict things as well:  root@debian:~ # echo $HOSTTYPE i486  root@debian:~ # getconf LONG_BIT 32 I've tried to render my scene but there's an object that won't show up. I've checked the camera, I've checked the visibility, it isn't hidden and it's showing in the viewport. I feel like I've opened every setting and have achieved nothing. I’m trying to render a book with a cover, flipping pages and stacks of pages. I have no idea how to fix the fact that the book cover doesn’t render. If I create a plane and select both the book cover and the plane and join them with Ctrl+J, the render contains a book cover but it doesn’t turn as it’s rigged to do so because it’s now linked to the plane and loses all the animated properties. As soon as I unjoin them the book cover stops rendering and everything appears as you see it there, a book with binding, pages, but no cover. For the life of me I cannot figure out what’s going on. There's a link to the file here: Persistent live drive with a partition for persistence There are some web sites describing  new tools new features in [new versions of] old tools  that can create a persistent live drive from an iso file with Ubuntu 19.10 and the corresponding Ubuntu family flavours.  Why and how does it work? How is it different from earlier methods for persistent live drives? Isn't live the default for a cloned drive? JavaScript: getting ImageData without canvas Can't access select https sites on Linux over PPPoE My internet connection used to be a direct LAN connection to my provider. Back then, everything would load fine on both Windows and Ubuntu (dual boot). However, a while ago they started needing me to dial (PPPoE) using a username and password. Gateway, subnet mask, IP, DNS servers all stayed the same. But since then, I haven't been able to browse certain websites on Ubuntu, even though there have been no such issues on Windows. Some example websites are -  (although share.ovi.com loads fine, and nokia.com loads fine),  (works on Chrome(ium) and Opera but not on Firefox (both 3.6 and 4)) Mozilla  and other random websites.  Some of the websites that don't load show timeout messages and for some websites (like the moz addons one), the browser will keep trying to load without an end (I've left it like that even for hours but not noticed anything different happen).  I have tried changing the DNS servers to public ones. I have even tried booting from a Fedora LiveCD and then changing the DNS to those (and even to the ones of OpenDNS), but the exact same thing happens. What could be inherently wrong with some config within Linux itself that is causing this problem?  Does anyone know why this is happening and how it can be fixed?  Note: This question has been  on SU, but not gotten any responses.  Update: Just saw  that someone else was having similar problem and solved it by putting a NetworkManager.conf file in /etc/NetworkManager. What needs to be in that file?