I think the strategy for this problem would be i assume some arbitrary element is in gcd(a,b) and chase it into the rhs and then do it the other way around , but i am not sure how to even start this one.
Let $D$ be a , and let $a,b,x \in D \setminus \{0\}$. Then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$ ?    Let $c=\gcd (a,b)$ and $d=\gcd(ax,bx)$, then as $cx|ax$ and $cx|bx$ so $cx|d$. We would be done if we could show $d|cx$, but I am unable to show that. Please help me to solve this problem.
I found  post about how to do Crow's Foot ERM Diagrams with Tikz, but it looks strange because the entity is outside the frame. However, it worked.  Then I found  even nicer version and tried to combine it, but sadly I'm not able to find out why it doesn't work. I'm not able to print two entities side by side and connect them with a crow's foot wire. They always print over each other...  How can I have both the lines and the style?  \documentclass{article}  \usepackage{tikz} \usetikzlibrary{shapes.multipart} \usetikzlibrary{matrix} \usetikzlibrary{positioning} \usetikzlibrary{shadows} \usetikzlibrary{calc}  \tikzset{     entity/.code={         \tikzset{             rounded corners,                          name=#1,             inner sep=2pt,             every entity/.try,         }%         \def\entityname{#1}%     },     entity anchor/.style={matrix anchor=#1},     every entity/.style={             draw,     },     every property/.style={         inner xsep=0.20cm, inner ysep=0.075cm, anchor=west, text width=1.75in     } } \def\property#1{\node[name=\entityname-#1, every property/.try]{\propertysplit#1;};} \def\properties{\begingroup\catcode`\_=11\relax\processproperties} \def\processproperties#1{\endgroup%     \gdef\propertycode{}%     \foreach \p in {#1}{%     \expandafter\expandafter\expandafter\gdef\expandafter\expandafter\expandafter\propertycode%             \expandafter\expandafter\expandafter{\expandafter\propertycode\expandafter\property\expandafter{\p}\\}%     }%     \propertycode% } \def\propertysplit#1:#2;{#1:\hfill#2}  \def\entitynamenode{% \node[every entity name/.try] (\entityname-name) {\entityname}; \draw (\entityname-name.south west) -- (\entityname-name.south east); \\[1ex] } \tikzset{   every entity name/.style={every property/.try, align=center} } \begin{document} \begin{tikzpicture}[every node/.style={font=\ttfamily}, node distance=0.5in] \matrix (m1) [entity=Employee] {     \entitynamenode     \properties{         Username:,         Password :  varchar(255),                 Name :  varchar(255),         LastName :  varchar(255)     } }; \matrix (m2) [entity=Student] {     \entitynamenode     \properties{         Username:,         Password :  varchar(255),                 Name :  varchar(255),         LastName :  varchar(255)     } }; \draw [-&gt;] (m1) -- (m2); % &lt;-- it break's here... %\draw [one to omany] (Employee-Username:) to node[above]{label} (Student-Username:); \end{tikzpicture} \end{document}      Edit: this is a Crow's Foot Notation for visualizing IT Database structures: I'm new to blender and have been studying and starting with low poly modeling. Recently I changed my GPU from a GTX 960 to an RX 580. I uninstalled the drivers and installed new ones using DDU.  Problem: Rendering using OpenCL produces these unwanted lines. The attached image is a product of CPU + GPU render then the GPU only render, respectively. When I render using only the CPU the results are as expected, no unwanted black vertical lines, using only the GPU adds more lines on the image.  Any help is appreciated, thank you! If you True Polymorph a zombie you create via Finger of Death, does it remain under your command? When you kill a humanoid with Finger of Death, it creates a zombie that is permanently under your command.  If you then True Polymorph that zombie, replacing its statistics with another creature's, does the creature remain under your control?  Related: Can some one explain this terminology please I think I understand it but not completely sure.   I think pull down is where you place a resistor between +V and the other component and pull up is where you place the resistor between 0v and the component.    If I am completely wrong then let me know! LaTeX errors in Formatting I want to print this text :  make -j 5 KDEB_PKGVERSION=1.yourcustomname deb-pkg  But I feel because of the underscore , LaTeX generates an error missing $ inserted and it doesn't print it as well.  Secondly, In the \fbox{} , I wanted to print the two texts on the next line(i.e) one text per line , so I used \ and even \par but it doesn't seem to work and I would like to align the (or) as well.   \fbox{\texttt{uname -a}\\(or) \texttt{cat /proc/version}}   Here is my full source code:  \documentclass[12pt]{article} \author{Subham Soni S.} \date{\today} \title{Compiling and Installing a Kernel 3.13.3 On Ubuntu, Debian and its Derivatives} \begin{document} \maketitle To replace the existing \textsl{kernel} with a new one, do the following: \begin{enumerate} \item Create a folder named \emph{kernel} in the home directory. \item Download the latest kernel to the folder from  \texttt{www.kernel.org}. \item Extract the file. \item In the terminal, type the following command to \textbf{install the neccesary tools to compile the kernel}:   \begin{center}     \fbox{\texttt{sudo apt-get install gcc libncurses5-dev dpkg-dev}}   \end{center} \item Enter the directory of the extracted kernel source   \begin{center}     \fbox{\texttt{cd kernel} \par \texttt{cd linux-3.13.3}}   \end{center} \item Configure the kernel   \begin{center}     \fbox{\texttt{make menuconfig}}   \end{center}   In this menu you can customize your kernel \item Save and exit \item Compile the kernel   \begin{center}     \fbox{\texttt{make -j 5 KDEB_PKGVERSION=1.yourcustomname deb-pkg}}   \end{center}   \emph{This process might take a while...} \item Install the kernel   \begin{center}     \fbox{\texttt{sudo dpkg -i ../linux*.deb}}   \end{center} \item Reboot   \begin{center}     \fbox{\texttt{sudo reboot}}   \end{center} \item Run the following commands to check the kernel version   \begin{center}     \fbox{\texttt{uname -a}\\(or) \texttt{cat /proc/version}}   \end{center} \item You can easily uninstall the kernel with the command:   \begin{center}     \fbox{\texttt{sudo apt-get purge linux-image-3.13.3 linux-image-3.13.3-dbg}}   \end{center} \end{enumerate} \end{document} $n$-th digit in the sequence of natural numbers What's the $n$-th digit in the sequence $S$ of numbers formed by the natural numbers, i.e.,  $n$-th digit in the sequence 1 2 3 4 5 6 7 8 9 10 11 12... ? For example 11th digit in the sequence is 0. is it possible to combine two fields in one and use that field to group by in reports? for example, i would like to combine ee id and ee name fields in 1 and show as 1 field in the "group by" section on reports. Obtain user and kernel time of a running process? Is there way to determine using standard Linux/Unix tools how much a process has spent in User mode and how much waiting for kernel?  In other words, exactly the "user" and "sys" values that you get when using time, but during process runtime?  NOTE: one way is to use WBEM and enumerate Linux_UnixProcess, but I need to use other tool than this; my aim is to verify what WBEM provider tells me, i.e. I need to use different tool. Which is faster/best? SELECT * or SELECT column1, colum2, column3, etc Are there 'stack' sites for Mac or Windows? The formula for a one sample t-test, as given by  is  $t = \dfrac{\bar{x} - \mu_0}{s\big/\sqrt{n}}$  However, in this equation, if the sample standard deviation, $s$, is zero, $t$ will be undefined. Is there any reasonable way to get a $t$ value in this case? Can all fundamental forces be fictitious forces? Details on how the Yearling badge works Jawa asked me this  and I didn't know the answer. So I present it to the meta SO community:     [To get the Yearling badge] Do you need to earn the 200 rep within that one year or is it enough to get 200 at some point after being a member for a year? And does 'a year' mean the very first 12 months or the last (sliding window of) 12 months?    I would assume that if you hit 200 reputation after you've already been around for a year, then you would get the Yearling badge. But I don't know. Why my differential equations become True? Why couldn't they omit the Batgirl narratives and scene in The Killing Joke movie? I loved the comic book. I've read it multiple times. And given that the purpose of the book and consequently, the movie, was       for the Joker to prove that anyone can be driven mad simply because of "one bad day", all he needed was the Commissioner right?    Why would they need to have us, as viewers, bond with Batgirl emotionally for around 25-30 minutes, have her frolic around with Batman and try to prove herself to him, etc.?     Sure, you feel deep sorrow for Barbara when she gets shot and molested by Joker. And this obviously is what affects Commissioner Gordon (in part),   But it isn't essential to the crux and the essence of the movie in my opinion (and going by the book, so to speak). Did Sam Liu or Brian Bolland offer any explanation to this end? crossfade between 2 videos using ffmpeg My eth0 has gone and I don't have internet and network connection I had internet connection, but when I upgraded my VGA and restarted my PC then everything for eth0 has gone.     When I used ifdown:     ifdown: interface eth0 not configured   Is there something I could do?    EDIT: Content of /etc/network/interfaces    auto lo iface lo inet loopback   When I ifconfig I don't have these lines:    inet addr:192.168.1.5  Bcast:192.168.1.255  Mask:255.255.255.0 inet6 addr: fe80::219:5bff:fe5e:a5e/64 Scope:Link   In the Terminal typed:  sudo gedit /etc/network/interfaces   and then added these lines in the bottom:  auto eth0 iface eth0 inet dhcp   then I typed:    sudo ifdown eth0 sudo ifup eth0   when I send the second command I received the below message:    No DHCPOFFERS received No working leases in persistent database - sleeping   Any help? Calculation of pressure from flow rate of water Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm diameter pipe, what will be the pressure generated by water? Why separation of variables works in PDEs? To reopen a closed question,  must agree that the question is suitable for the site and cast votes to reopen the question. But:  How does one actually vote to reopen? Is there a reputation level that you must have before you can see this function? Or do I just leave a comment along the lines of, &quot;I vote to reopen&quot;? What happens if someone with less than 3000 reputation leaves a comment that they wish to vote to reopen? How can one draw attention to their closed questions? Is it done via a posting new question? Or do you edit the closed question?   Related:  For more information, see &quot;&quot; in the .