Prove using contradiction that any prime number greater than $3$ is of the form $6n \pm 1$.  Thanks for any help
Show that every prime $p&gt;3$ is either of the form $6n+1$ or of the form $6n+5$, where $n=0,1,2, \dots$
How do I share an ethernet connection via wifi on Windows 8? I have a Windows 8 laptop that is connected to a router via Ethernet. I want to make the laptop act like a wireless router via wifi so that other devices could connect to the computer using wifi and gain access to its Ethernet internet connection.  How do I do something like this? Key uses weak digest algorithm I'am getting this kind of message while updating my ubuntu 16.04 LTS:  W: http://dl.google.com/linux/chrome/deb/dists/stable/Release.gpg: Signature by key 4CCA1EAF950CEE4AB83976DCA040830F7FAC5991 uses weak digest algorithm (SHA1) W: http://dl.google.com/linux/chrome/deb/dists/stable/Release.gpg: Signature by key 3B068FB4789ABE4AEFA3BB491397BC53640DB551 uses weak digest algorithm (SHA1)   Can anyone help me? Injecting beans into a class outside the Spring managed context I'm an end-user of one of my company's products. It is not very suitable for integration into Spring, however I am able to get a handle on the context and retrieve the required bean by name.  However, I would still like to know if it was possible to inject a bean into this class, even though the class is not managed by Spring itself.  Clarification: The same application which is managing the lifecycle of some class MyClass, is also managing the lifecycle of the Spring context. Spring does not have any knowledge of the instance of MyClass, and I would like to some how provide the instance to the context, but cannot create the instance in the context itself. For a book cover, I want to write the title vertically (like in Japanese, but using English text):           T T        I H        T I  I  M  L S  S  Y  E   How do I do this without jumping through a host of \vbox and \hboxes? How do I fix a "Problem with MergeList" or "status file could not be parsed" error when trying to do an update? How can I capture the movement of a bullet? Just beginning with photography.    Consider this image:     (This photo was taken by Harold "Doc" Edgerton in 1964 using his Rapatronic camera.)  I am looking for a  camera that can capture such an image. I am not looking for more fps. less fps is fine, but it must be able to capture such an instance.   What features should I look in such a camera?  How fast should be the shutter speed? What other things I should look for? Which merchants pay best? I noticed at some point that different merchants don't all pay the same for what you're selling. Depending on the category, or even the specific item, some merchants simply pay significantly more.  Are there some general rules on which merchants pay better for which items? Dealing with non-integral powers on negative numbers If we are given an expression $(-8)^\frac26$, how do we solve it?  If it is $(-8)^\frac13$, we can find the cube root of -8 which is -2. However, if we square it first and find the sixth root, we get +2 (or maybe $\pm2$, which still isn't the same as just -2.  Also realised that when solving logarithmic and exponential questions, I had often made the assumption that if $b^a=b^c$, then $a=c$, either explicitly, or via some formula. I don't know if this is really true now.  So is there some convention by which we solve non-integral powers or is it just undefined to do so or something?  P.s. Talking of non-integral powers, will a quantity like $(-8)^{√3}$, will it be positive or negative. (Basically that's an irrational power now.) I suspected that installing xfce4 cause some issues in Ubuntu so I removed them using apt-get remove xfce4 xfce4-goodeis.  But when I ran 'dpkg -l' I still can see some libraries and packages for xfce4:  $ dpkg -l | grep -i xfce rc  libexo-1-0:amd64                              0.10.2-2                                 amd64        Library with extensions for Xfce rc  libgarcon-1-0                                 0.2.1-1                                  amd64        freedesktop.org compliant menu implementation for Xfce rc  libxfce4ui-1-0                                4.11.0-0ubuntu1~ppa0.13.10.1             amd64        widget library for Xfce - Gtk+2 variant rc  libxfce4ui-common                             4.11.0-0ubuntu1~ppa0.13.10.1             all          common files for libxfce4ui rc  libxfce4util6                                 4.10.1-1                                 amd64        Utility functions library for Xfce4 rc  libxfcegui4-4                                 4.10.0-2                                 amd64        Basic GUI C functions for Xfce4 rc  libxfconf-0-2                                 4.10.0-2                                 amd64        Client library for Xfce4 configure interface rc  mousepad                                      0.3.0-2                                  amd64        simple Xfce oriented text editor rc  thunar                                        1.6.3-1ubuntu1                           amd64        File Manager for Xfce rc  xfce4-appfinder                               4.10.1-1                                 amd64        Application finder for the Xfce4 Desktop Environment rc  xfce4-clipman                                 2:1.2.3-2ubuntu1                         amd64        clipboard history utility rc  xfce4-mixer                                   1:4.10.0-1ubuntu2                        amd64        Xfce mixer application rc  xfce4-notes                                   1.7.7-3ubuntu2                           amd64        Notes application for the Xfce4 desktop rc  xfce4-panel                                   4.10.1-1ubuntu1                          amd64        panel for Xfce4 desktop environment rc  xfce4-power-manager                           1.2.0-2ubuntu1                           amd64        power manager for Xfce desktop rc  xfce4-session                                 4.10.1-1ubuntu1                          amd64        Xfce4 Session Manager rc  xfce4-settings                                4.11.1-0ubuntu1~ppa0.13.10.1             amd64        graphical application for managing Xfce settings rc  xfce4-terminal                                0.6.2-3ubuntu1.1                         amd64        Xfce terminal emulator rc  xfce4-volumed                                 0.2.0-0ubuntu1                           amd64        volume keys daemon rc  xfdesktop4                                    4.11.2-0ubuntu1~ppa0.13.10.1             amd64        xfce desktop background, icons and root menu manager rc  xfwm4                                         4.11.1-0ubuntu1~ppa0.13.10.1             amd64        window manager of the Xfce project   I copy-pasted all these packages\libraries to form an apt-get remove command to remove all of these dependencies, and the command ran normally, but running dpkg -l | grep -i xfce showed these dependencies again !  Why are these dependencies still installed ? how to not commence a command depending on player health? What would you call a word that doesn't exist in or translate well into another language? uwsgi errno 24 too many open files on CentOS / nginx Difference between staticmethod and classmethod What is the difference between a function decorated with  and one decorated with ? I use Lyx 2.1, document class : Report. My problem is that the titles of figures are written on the numbers at List of Figures. $1 \leq z \overline {z} \leq 4$ and $|\Im(z)|&lt;\Re (z)$  How can I solve this system of inequalities? ($\Im$ is the imaginary part and $\Re$ is the real part of a complex number).  I have tried so far: $z=x+yi$ and then I get $1 \leq x^2+y^2 \leq 4$ and $ |y|&lt;x$. How can I solve this? Find duplicate records in MySQL How will multiple GPUs improve Cycles' rendering performance? I have an NVIDIA Titan GPU and I'm able to add another card, but I wonder whether  Blender will benefit from more than one GPUs?  Should I do it as SLI or should I just do it as an added card? I just need some help in understanding how Blender will use either SLI or a second GPU.  Note that I only use Cycles. Beamer: How to Disable `\pause` Temporarily Using uniform coloring in MatrixPlot Is there an easy method for installing binary builds of glibc? Time and time again I see questions such as these:       And these are the types of solutions we're typically pushing:        Is this really the best we can do? Aren't there binary builds of GLIBC that we can simply unzip into a directory such as /opt/myglibc, and set the $LD_LIBRARY_PATH or whatever and run whatever application we want, without issues?   An application, such as the newer builds of Chrome (28+) that appear to require GLIBC 2.14?  NOTE: This thread titled:  on tecmint.com is what ultimately got me thinking about this.  References