If $a = r \pmod b$ when $0 \le r < b$, then $\gcd(a, b) = \gcd (b, r)$
Why $\gcd(qb+r,b)=\gcd(b,r)$?
How can I know when my screen was locked last time? Exist a log where I can look for that information? I want to know last days when my PC automatically locked the screen because was idle. Which answer do I accept if I have multiple correct answers? Block apps from accessing the Internet on Android device In Android, is it possible to block apps from accessing the Internet? Many apps will often connect to remote servers in the background, including Google's own apps or system services. Over time this can eat away at a user's data limit set by a mobile carrier. Does Android allow an app to act as a firewall whereby the user can select which apps have access to the Internet? Or does the device have to be rooted to have that ability? Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$? How can I get the page title? Strange arrow mark with TikZ edge and anchors. When I draw an edge between two nodes with anchors and globally set option [-&gt;], I get an additional arrow tip symbol at the beginning of the last edge in the path. For example in  \documentclass{article} \usepackage{tikz}  \begin{document} \begin{tikzpicture}     \node (A) at (0,0) {$A$};     \node (B) at (1,0) {$B$};      \draw[-&gt;] (A.north east) edge (B.north west);      \draw (A.south east) edge[-&gt;] (B.south west); \end{tikzpicture} \end{document}   the first \draw command produces incorrect output, while the second produces correct output:    Am I doing something wrong, or is this a bug in TikZ? Can a JavaScript object have a prototype chain, but also be a function? function a () {     return "foo"; }  a.b = function () {     return "bar"; }  function c () { }; c.prototype = a;  var d = new c(); d.b(); // returns "bar" d(); // throws exception, d is not a function   Is there some way for d to be a function, and yet still inherit properties from a? How to prevent RGB composite flatten to 1 band after raster calculation I have a series of landsat wanting to process in raster calculator, but after doing the tool it happened these output images only contain one single band. They used to be RGB 3-band images.  It is on arcmap 10.3. I was using raster calculator to remove a certain value in my 3-band landsat image. After I type in the conditional statement to remove all 0 value from the inpur RGB image, it only returns an image of 1band, black and white. How can I preserve the RGB value in output. Does anyone know the name of travel posters from the 1930s? Enlarged partition, filesystem still reports old size How can I find the name of a Package? Why is "bicycle" pronounced differently from other obviously related words? I want to show that if a function $f:[a,b]\rightarrow \mathbb R$ satisfies a Hölder condition of order $\alpha &gt; 1 $ then it is constant.  The way I think of it is as follows:  $$|f(x) - f(y)| &lt; K|x-y|^\alpha$$  $$\frac{|f(x) - f(y)|} {|x-y]}  &lt; K|x-y|^{\alpha -1}$$  $$\lim_{y\rightarrow x} \frac{|f(x) - f(y)|} {|x-y]} \le \lim_{y\rightarrow x}  K|x-y|^{\alpha -1} =0 $$ As the limit is $0$, we can remove the modulus, so we get:  $$\lim_{y\rightarrow x} \frac{f(x) - f(y)} {x-y} = 0$$ So $f$ is derivable and $f'(x) = 0$ for all $x$ in $[a,b]$. Note that the reason we can add the limit $y\rightarrow x$ is because $[a,b]$ is closed in $\mathbb R$.  However, the question gives as a hint using the mean value theorem. I am not sure why one should do that. You would first have to prove that $f$ is derivable in a similar manner to what I did, and then prove that $f$ is constant. Or is there a simpler way to do it and I am missing it?  Also please inform me of any mistakes I did in the proof (if any)/ Thank you! SUID-bit not working for executables within /tmp directory Printing the value of getuid() and geteuid() from an executable with SUID-bit (chmod +s) turned-on, seems to result with the original caller ID instead of the owner id if the executable is located within the /tmp directory.  When compiling the exact same code to home directory (and executing chmod +s), this seems to work as expected.  I've searched a lot and could not find any reference to such behavior.  Does anybody know why is this happening?  this source is simple as that:  #include &lt;stdio.h&gt; #include &lt;stdlib.h&gt; #include &lt;sys/types.h&gt; #include &lt;unistd.h&gt;  int main(){     printf("%d\n%d\n", getuid(), geteuid());     return 0; } Extend tourist visa stay in USA due to coronavirus and waive I-539 fee My mom has come to US on a tourist visa and her I-94 expires on the first week of May.   Due to the coronavirus, travel restrictions have been imposed in our home country (India). Also we want to avoid the risk of traveling in flights at this time.  Is there an easy way to to extend her stay in the US by one or two months?  I am aware that we should fill out an  to extend our stay. But in-order to submit the online application it requires a fee of $370.    Is filing I-539 the easiest way to extend her stay at this time? If so, is it possible to waive the fee due to the coronavirus situation?  After filing I-539 should she wait for an approval to continue her stay? Or is the receipt good enough?   Can you please help me with these? Thanks!  [Edit 1]:  With the current situation of the virus, traveling anywhere sounds like a very risky operation, especially for elders.   That is the main reason behind this question. If the US government will allow visitors to overstay until Covid-19 settles down! How do I detach a process from Terminal, entirely? I use Tilda (drop-down terminal) on Ubuntu as my "command central" - pretty much the way others might use GNOME Do, Quicksilver or Launchy.  However, I'm struggling with how to completely detach a process (e.g. Firefox) from the terminal it's been launched from - i.e. prevent that such a (non-)child process   is terminated when closing the originating terminal  "pollutes" the originating terminal via STDOUT/STDERR   For example, in order to start Vim in a "proper" terminal window, I have tried a simple script like the following:  exec gnome-terminal -e "vim $@" &amp;&gt; /dev/null &amp;   However, that still causes pollution (also, passing a file name doesn't seem to work). Identifying pin numbers from PCB Error: The processing instruction target matching "[xX][mM][lL]" is not allowed Spoilers for A Storm of Swords / Season 4 episode 2 "The Lion and the Rose".  At the Purple Wedding,      Littlefinger and Lady Olenna Tyrell   perform their plan of      poisoning King Joffrey.   A short summary of their plan:  Littlefinger orders Ser Dontos Hollard to give Sansa Stark a beautiful silver hairnet adorned with amethysts. At least some of the amethysts are actually strangler crystals in disguise. Ser Dontos also, still under orders of Littlefinger, urges Sansa to wear the hairnet at the wedding, which she then does. At the wedding, when Lady Olenna greets Sansa, she fusses her hairnet a bit, while secretly taking one of the strangler crystals. Later, during the wedding, Lady Olenna puts the crystal in Joffrey's royal cup, poisoning him.  But why was their plan so complicated? Why couldn't Lady Olenna just bring a strangler crystal with her to the wedding (as suggested in )?  Then they wouldn't depend on Ser Dontos and Sansa who could unknowingly have done something to prevent the success of the plan.  The only reason that I could think of, is Littlefinger and Lady Olenna plan for Sansa (and Tyrion as her husband with her) to take the blame for Joffrey's death.  They put the crystals on her person, so that upon examination it would clearly show that Sansa had the murder weapon on her. But Littlefinger had a plan he did not tell Lady Olenna, namely rescuing Sansa during the chaos ensuing the murder (and thereby leaving Tyrion behind as the only accused).  Is there anything confirming or debunking this theory? If my theory doesn't hold up, is there another explanation for why the plan was so needlessly complicated? Some verbs are followed by ing, e.g. I enjoy swimming. We can't say I enjoy to swim. Likewise, some verbs are followed by to, e.g. I decided to make a plan.   Which particular verbs are followed by ing and to? Can you please provide a list for that?  Moreover, which verbs can be followed by both without having the meaning changed?