Does Euclid's Lemma apply to squared numbers?
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
How can I get ssh-agent working over ssh and in tmux (on OS X)? I have a private key set up for my github account, the passphrase to which is, I believe, stored in OS X's keychain. I certainly don't have to type it in when I open a terminal window and enter ssh git@github.com.  However, when I'm running bash over an ssh session, or locally inside a tmux session, I have to type in the passphrase every single time I attempt to ssh to github.   suggests that a similar problem exists with screen, but I don't really understand the issue well enough to fix it in tmux. There's also  which includes a fairly complicated solution, but for zsh.  EDIT:  In response to , from a local terminal I get the following output:  [~] $ echo $SSH_AUTH_SOCK /tmp/launch-S4HBD6/Listeners [~]  $ ssh-add -l 2048 [my key fingerprint] /Users/richie/.ssh/id_rsa (RSA) [~] $ typeset -p SSH_AUTH_SOCK declare -x SSH_AUTH_SOCK="/tmp/launch-S4HBD6/Listeners"   Whereas over ssh or in tmux I get:  [~] $ echo $SSH_AUTH_SOCK  [~] $ ssh-add -l Could not open a connection to your authentication agent. [~] $ typeset -p SSH_AUTH_SOCK bash: typeset: SSH_AUTH_SOCK: not found   echo $SSH_AGENT_PID returns nothing whatever shell I run it from. dpkg exit with error parsing file `/var/lib/dpkg/status`, what to do? When I try to install any software, I encounter this error, and therefore I cannot update.  Preconfiguring packages ... dpkg: error: parsing file '/var/lib/dpkg/status' near line 51245 package 'oracle-xe':  mixed non-coinstallable and coinstallable package instances present N: Ignoring file 'gcl' in directory '/etc/apt/sources.list.d/' as it has no filename extension N: Ignoring file 'gcl' in directory '/etc/apt/sources.list.d/' as it has no filename extension E: Sub-process /usr/bin/dpkg returned an error code (2) Install apt package in ubuntu 12.04 I have mistakenly removed the default package APT from my system .  When I run command locate apt-get, I get below output:  /home/jeet/apt-get /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/cmdline/apt-get.cc /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/apt-get.8.xml /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/de/apt-get.de.8 /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/fr/apt-get.fr.8 /home/jeet/Desktop/apt/apt-0.7.25.3ubuntu9.13/doc/ja/apt-get.ja.8 /home/jeet/Downloads/apt-get /home/jeet/Downloads/apt-get.8.gz /usr/share/bash-completion/completions/apt-get /usr/share/bash-completion/completions/slapt-get   If I run ls | grep apt-get, then I won't get any output.  Can anybody please advice how to recover apt package or install it from start? How to generate XML file dynamically using PHP? I have to generate a xml file dynamically at runtime. Please help me in generating the below XML file dynamically using PHP.  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;xml&gt;  &lt;track&gt;      &lt;path&gt;song1.mp3&lt;/path&gt;      &lt;title&gt;Track 1 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song2.mp3&lt;/path&gt;      &lt;title&gt;Track 2 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song3.mp3&lt;/path&gt;      &lt;title&gt;Track 3 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song4.mp3&lt;/path&gt;      &lt;title&gt;Track 4 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song5.mp3&lt;/path&gt;      &lt;title&gt;Track 5 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song6.mp3&lt;/path&gt;      &lt;title&gt;Track 6 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song7.mp3&lt;/path&gt;      &lt;title&gt;Track 7 - Track Title&lt;/title&gt;  &lt;/track&gt;  &lt;track&gt;      &lt;path&gt;song8.mp3&lt;/path&gt;      &lt;title&gt;Track 8 - Track Title&lt;/title&gt;  &lt;/track&gt; How to perform entity validation on code level? I have an entity that has a field attached to it and the values that user types into the field has to be globally(website) unique(compared to other entities).  I have added validation to the entity form but what if I create this entity programmatically? How can I prevent the entity to be saved into the storage?  I've noticed there is a validate method in ContentEntityBase, though not in ConfigEntityBase. Is this the place for it? If so, I could use some examples. Installing Teamspeak and creating TeamSpeak3 .desktop file I am very new to Ubuntu and I want to create desktop launcher.  I have this in my TeamSpeak3.desktop in   [Desktop Entry] Name=TeamSpeak 3 Comment=TeamSpeak 3 VoIP Communicator Exec=/opt/TeamSpeak3-Client-linux_amd64/ts3client_runscript.sh Terminal=false Type=Application Categories=Network;Application; Icon=/opt/TeamSpeak3-Client-linux_amd64/styles/default/logo-128x128.png   in my ~/.local/share/applications/TeamSpeak3.desktop But I dont see it in my launcher and when I double click on it files, it just opens the text file. I even made it executable with     chmod +x TeamSpeak3.desktop  drwx------ 15 hung hung     4096 srp 16 12:29 . drwxr-xr-x  3 root root     4096 pro  9 19:22 .. -rw-------  1 hung hung   174627 srp 16 12:29 CHANGELOG -rwx------  1 hung hung   227136 srp 16 12:29 error_report drwx------  2 hung hung     4096 srp 16 12:29 gfx drwx------  3 hung hung     4096 srp 16 12:29 html drwx------  2 hung hung     4096 srp 16 12:29 iconengines drwx------  2 hung hung     4096 srp 16 12:29 imageformats -rwx------  1 hung hung   334520 srp 16 12:29 libc++abi.so.1 -rwx------  1 hung hung  1934744 srp 16 12:29 libcrypto.so.1.0.0 -rwx------  1 hung hung   746960 srp 16 12:29 libc++.so.1 -rwx------  1 hung hung  5842312 srp 16 12:29 libQt5Core.so.5 -rwx------  1 hung hung   484832 srp 16 12:29 libQt5DBus.so.5 -rwx------  1 hung hung  5683224 srp 16 12:29 libQt5Gui.so.5 -rwx------  1 hung hung  1335584 srp 16 12:29 libQt5Network.so.5 -rwx------  1 hung hung   290008 srp 16 12:29 libQt5Positioning.so.5 -rwx------  1 hung hung  3829280 srp 16 12:29 libQt5Qml.so.5 -rwx------  1 hung hung  3831288 srp 16 12:29 libQt5Quick.so.5 -rwx------  1 hung hung   234552 srp 16 12:29 libQt5Sql.so.5 -rwx------  1 hung hung   331232 srp 16 12:29 libQt5Svg.so.5 -rwx------  1 hung hung   117104 srp 16 12:29 libQt5WebChannel.so.5 -rwx------  1 hung hung 67570152 srp 16 12:29 libQt5WebEngineCore.so.5 -rwx------  1 hung hung   208344 srp 16 12:29 libQt5WebEngineWidgets.so.5 -rwx------  1 hung hung  6439120 srp 16 12:29 libQt5Widgets.so.5 -rwx------  1 hung hung  1334528 srp 16 12:29 libQt5XcbQpa.so.5 -rwx------  1 hung hung   180248 srp 16 12:29 libquazip.so -rwx------  1 hung hung    22936 srp 16 12:29 libsnappy.so.1 -rwx------  1 hung hung   111888 srp 16 12:29 libsrtp.so.0 -rwx------  1 hung hung   383072 srp 16 12:29 libssl.so.1.0.0 -rwx------  1 hung hung    51080 srp 16 12:29 libudev.so.0 -rw-------  1 hung hung     4340 srp 16 12:29 openglblacklist.json -rwx------  1 hung hung   260232 srp 16 12:29 package_inst drwx------  2 hung hung     4096 srp 16 12:29 platforms -rw-------  1 hung hung       26 srp 16 12:29 qt.conf drwx------  2 hung hung     4096 srp 16 12:29 qtwebengine_locales -rwx------  1 hung hung    19720 srp 16 12:29 QtWebEngineProcess drwx------  2 hung hung     4096 srp 16 12:29 resources drwx------  6 hung hung     4096 srp 16 12:29 sound drwx------  2 hung hung     4096 srp 16 12:29 soundbackends drwx------  2 hung hung     4096 srp 16 12:29 sqldrivers drwx------  3 hung hung     4096 srp 16 12:29 styles drwx------  2 hung hung     4096 srp 16 12:29 translations -rwx------  1 hung hung 18987008 srp 16 12:29 ts3client_linux_amd64 -rwx------  1 hung hung     1364 srp 16 12:29 ts3client_runscript.sh -rwx------  1 hung hung  2206064 srp 16 12:29 update drwx------  2 hung hung     4096 srp 16 12:29 xcbglintegrations Determine if wire in switch box is safe to re-purpose? I need to pull a neutral wire to my light switch for a smart switch.  It's presently switching an outlet that I don't need switched, and the other side of the outlet already has unswitched power.  My plan is to use a smart switch, which requires neutral, to control a different device wirelessly.    I can't feasibly run a new wire, because the wires aren't run through conduit.  Instead, my plan is to repurpose the switched wire to get neutral from the outlet.    The switch, which controls an outlet has two wires, one black and one red.  The switched outlet has a white neutral wire, plus the red and black wires that I assume run directly to the switch.  I've completely disconnected the red and black wires from the outlet and the switch.  The black wire is measuring 120V AC when measured against ground using the box as ground, both at the outlet and at the switch. Using my DMM, the red wire is measuring 24V AC with respect to the box/ground at both sides.  I assume this is a  caused by induction from the charged black wire over to the floating red wire.    Our house is ~100 years old and this particular switch seems to be run using armored cable (note the paper wrap around each wire.)  There are literally only two wires in the switch box; no wire nuts.    If relevant, we do have some old knob and tube wiring active, but I'm pretty confident there's none on this circuit.  Is there some way I can determine with enough confidence that the red wire isn't connected elsewhere such that I can know it's safe to connect the red wire at the outlet to netural? Why do only Hobbits use a combination of first- and last names? While all the Hobbits I can think of have a combination of first- and lastname (e.g., Bilbo Baggins, Peregrin Took, the Sackville-Baggins's,...), I can't think of any character* of another race that has a lastname:   Men seem to like to add a reference to their ancestors (e.g., Aragorn, Arathorn's son or Isildur's heir) Dwarves seem to like descriptive or honorary names (e.g., Thorin Oakenshield, Dain Ironfoot). They are not lastnames though, since they do not get passed on to descendants. Elves don't have a need for lastnames, since elvish names are unique. Some nevertheless seem to have an additive (e.g., Legolas Greenleaf). Likewise, I can't find any usage of lastnames among Ents, Eagles, Istari, Orcs, trolls,...   But why would a society that is quite rural and not a leader of modernization be the only one to use a modern naming system with first- and lastnames?  *Except for Tom Bombandil. But he is, well, "special". Macbook Air - how to install a dual bootable Ubuntu 14.04 LTS On my Macbook Air 10.9.2 without crashing the current setup, how can i install as dual boot: Ubuntu 14.04 LTS ? (can anyone please advise some step by step please) Characterising reals with terminating decimal expansions Show that a number has a terminating decimal expansion if and only if, it is rational and when in lowest terms, its denominator is coprime to all primes other than $2$ and $5$.   This is an unsolved question in my lecture notes. I can only seem to prove the converse direction for this. Would appreciate a solution for the other direction.     For converse direction:   Let the number, in lowest terms, be given by $\frac{l}{m}$ where $m = 2^ \alpha 5^\beta$, for some positive integers, $\alpha$ and $\beta$.    If $\alpha &gt; \beta$, let $k = 5^{(\alpha-\beta)}$. If $\alpha &lt; \beta$, let $k = 2^{(\beta-\alpha)}$.   Then $\frac{l}{m} = \frac{kl}{k2^\alpha5^\beta}=\frac{kl}{10^q}$ where $q = \max(\alpha,\beta)$.   Hence $\frac{l}{m}$ is a terminating decimal. Fspy add-on not installing What are bitwise operators? I'm someone who writes code just for fun and haven't really delved into it in either an academic or professional setting, so stuff like these bitwise operators really escapes me.  I was reading an article about JavaScript, which apparently supports bitwise operations. I keep seeing this operation mentioned in places, and I've tried reading about to figure out what exactly it is, but I just don't seem to get it at all. So what are they? Clear examples would be great! :D  Just a few more questions - what are some practical applications of bitwise operations? When might you use them? Is there a way to adjust the torch/flash brightness level on an iOS device? Prove that the minimum number of cycles is $m-n+1$ The question I have is:   Prove that the minimum number of cycles is $m-n+1$ in a connected graph. Where one cycle is a path that starts that begins and ends at the same vertex. Where $m$ is edges and $n$ is the vertices.   I have no idea where to start. A few hints would be appreciated. Please do not provide me with the answer. apt-get install with '-' (minus / hyphen) removes packages I was looking for some package (nautilus-terminal), and accidentally did this:  $ sudo apt-get install nautilus- Reading package lists... Done                                                                                                                                                                                                  Building dependency tree                                                                                                                                                                                                       Reading state information... Done                                                                                                                                                                                              The following packages were automatically installed and are no longer required:                                                                                                                                                  apturl apturl-common libgail-3-0 linux-headers-4.4.0-57 linux-headers-4.4.0-57-generic linux-image-4.4.0-57-generic linux-image-extra-4.4.0-57-generic                                                                       Use 'sudo apt autoremove' to remove them.                                                                                                                                                                                      The following packages will be REMOVED:                                                                                                                                                                                          gnome-session-flashback nautilus nautilus-sendto nautilus-share ubuntu-desktop                                                                                                                                               0 upgraded, 0 newly installed, 5 to remove and 69 not upgraded.                                                                                                                                                                After this operation, 2 031 kB disk space will be freed.                                                                                                                                                                       Do you want to continue? [Y/n] ^[[^C                                                                                                                                                                                             That's quite dangerous because remove is much harder to mistype than a simple dash from a failed autocompletion.     Is that an equivalent of apt-get remove? I couldn't find any documentation for that. Edit: except for overlooking the man page... Using an NSString in a switch statement How is a Kelvin Pod different than a standard Escape pod? How to get back to a site when viewing one of its questions When viewing a question on a site which I don't use (I never registered on it), I can't figure out how to get back to the list of questions of the site.  See this example  from the Stack Exchange Android app. Where should I click to see the list of questions? (I chose Mathematics Educators because it's the most recent site, it is very likely that most users don't have an account on this website)  Here is a random example:    When viewing a question, I don't know how to view the list of questions. This site can't be found in the sidebar since it's not in my Your Sites list. The top menu containing the site's title only opens the sidebar. Is it possible to recover Classical Mechanics from Schrödinger's equation? Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the probability density of finding a particle in classical mechanics (using a Dirac delta function, perhaps)? Viruses: Adaptation to a new host through repeated host jumps