I understand that if the same message is sent to 3 people with $e=3$ that even with different public keys, the message can be decoded using the Chinese Remainder Theorem. I have tried to figure out the steps to do so, but I am unable to actually lay it out even using small numbers. How would one decrypt a message $m$ = 10, for example with $n_1=6$, $n_2=35$, and $n_3=143$, with $e=3$?
I have three different 1024-bit public keys with common exponent $e$ but different moduli. A message $m$ is encrypted (without padding) using the three keys, which results in three different encrypted messages.  Given the three pairs of public keys $(N_i,e)$ and the encrypted messages $c_i=m^e\bmod N_i$ , how do I decipher the original message $m$ ?
I'm trying to find the derivative of $\sin^{-1}(x)$. I know the steps that lead to $\frac{1}{\sqrt{1-x^2}}$, however I don't understand why the following reasoning leads to a wrong answer.  Because  $$\frac{d}{dx}f^{-1}(x) = \frac{1}{f'(f^{-1}(x))} $$  If we plug in for $f(x) = \sin(x)$, and because $\frac{d}{dx}\sin(x) = \cos(x)$ we get  $$\frac{d}{dx}\sin^{-1}(x) = \frac{1}{\cos(\sin^{-1}(x))} $$  Since $\sin(x) = \cos(x-\frac{\pi}{2})$, we can state that $\sin^{-1}(x) = \cos^{-1}(x-\frac{\pi}{2})$. (I suspect this is what is wrong)  Thus,  $$\frac{d}{dx}\sin^{-1}(x) = \frac{1}{\cos(\cos^{-1}(x-\frac{\pi}{2}))}$$  Then, by the definition of inverse function, we have  $$\frac{d}{dx}\sin^{-1}(x) = \frac{1}{x - \frac{\pi}{2}}$$ Look at this if block:  #!/bin/bash  str="m.m" if [[ "${str}" =~ "m\.m" ]]; then     echo "matched" else     echo "not matched"     exit 1 fi  exit 0   This should print "matched", but it doesn't. Where am I going wrong? If friction acts on car all time, why is it not accelerating forever? In the first gear, slowly releasing my clutch i push the gas pedal to the maximum torque level, say at 2000 rpm. Now as the engine torque is acting on the wheel, friction helps the car to accelerate.   If i hold the gas pedal at that position, the torque should continuously act on the wheel and the car should increase speed forever. But in reality even if we put the gas pedal at the max.torque rpm range in first gear it speeds up to certain wheel rpm (say 500rpm) and it stays there only. Why? I've done numerous WP sites, written my own plugins, run my own server, etc etc.  But I have not seen this before. I just installed a fresh 4.7.1 and installed the  and all its plugins.  When I went to add media files, I got:  Maximum upload file size: 2 KB.   I deactivated all plugins one by one...no dice. My PHP memory limit is set to 256MB for this installation via wp_config.php.  Googling the 2 KB limit turned up no results.   Anyone seen this before or know how to fix this limit? Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$. Let f(x) be a  polynomial satisfying $\lim_{x \to\infty} \frac{x^4f(x)}{x^8+1}=3,$  $f(2)=5 $ and $f(3)=10$, $f(-1)=2$ and $f(-6)=37$ . And then there are some question related to this. In the solution it is given that according to the given information, $f(x)$ is a polynomial of degree 4 with leading coefficient 3. $f(x)=3(x-2)(x-3)(x+1)(x+6)+(x^2+1)$ Now what i think is that he got the coefficient 3 using the limits and the rest of the terms$[(x-2)(x-3)(x+1)(x+6)]$ from the respective $f(x)$ values from what was given and also the $(x^2+1)$ was added for the remainders, as they satisfy all the values that have been given to us in the question. I just wanted to know if my approach is right? or is there another elegant way to do it?. about://(null) popup? I encountered a popup similar to this one this morning while checking the weather report at  in Safari, though I have not been able to reproduce it.  The title is "about://(null)" and the text "Why you no play Candy Crush!!"  The popup occurred twice.  I tapped Cancel both times.  I suspect the source of this is rogue JavaScript in an ad network, judging from the fact that the screenshot below shows it in an ad-supported application, and when I saw it, I was on an ad-supported website.  My phone is not jailbroken.  I'm wondering if anyone is able to identify the source of the popup definitively.  Speculation is running rampant on Apple's support communities and elsewhere, from push notifications (delete Facebook and all your games!) to carrier notifications (which don't work on iPod Touches…), and my gut tells me little of it is helpful.  But I could also be very wrong.  (This is not my screenshot; it comes from .)    UPDATE 1: The Candy Crush people have this to say, but I'm not (yet) convinced there's actually something installed that is to blame:   UPDATE 2: Just reproduced it in the iOS Simulator while clicking around woodtv.com, but I'm not sure how to track it down further from here. Pascal's triangle in tikz I would like to typeset the top part of Pascal's triangle. To get the triangle with the names of the binomial coefficients, i.e., {n \choose k}, I used the following code  \begin{tikzpicture} \foreach \n in {0,...,4} {   \foreach \k in {0,...,\n} {     \node at (\k-\n/2,-\n) {${\n \choose \k}$};   } } \end{tikzpicture}   The result is this   Now I want to be equally lazy and do something like this for the values of the binomial coefficients, i.e., replace {\n \choose \k} in the node label with \CalculateBinomialCoefficient{\n}{\k} where \CalculateBinomialCoefficient is a hypothetical macro that calculates the binomial coefficient. Has anyone done something like that?  The result should look like this: Stealing and reattaching a running process It's sunday and I left an instance of R running in the office. The script finished running, and I would like to save my workspace without going to the office. I can ssh to the computer, but I have not run the program into screen.  Is there a way, over ssh, to disown the process (I don't have access to jobsid of the terminal the program is running on!) and reattach it with say, reptyr? Reptyr and reptyr -T don't work without previously disowning the process  28845 3diag       20   0  139.3m  10.4m   0.0  0.1   0:12.06 S  `- urxvtd                                                                                        5327 3diag       20   0   16.4m   4.6m   0.0  0.1   0:00.02 S      `- bash                                                                                      5335 3diag       20   0 3499.3m 3.244g   0.0 43.3 171:57.89 S          `- R    The unique part of my question is that I explicitly require to detach a program without having access to the terminal in which it was created. I have a service (kado-demo.service) that a normal user (kado) should be able to restart without entering any password.   I created /etc/sudoers.d/user_restart and added  kado ALL=NOPASSWD: /bin/systemctl restart kado-demo.service   Permissions:  -r--r-----   1 root root   585 Mar  5 10:47 user_restart   As user k, I now should be able to execute the given command, but this happens:  /bin/systemctl restart kado-demo.service  ==== AUTHENTICATING FOR org.freedesktop.systemd1.manage-units ===  Authentication is required to restart 'kado-demo.service'.   Multiple identities can be used for authentication:   (...)   Which is the same result as before I added the file.   The /etc/sudoers contains  #includedir /etc/sudoers.d   And I even get the same result when I add content of the user_restart file directly to /etc/sudoers.  I'm running out of ideas... The Crumple-Horned Snorkack is one of various weird and wacky things which Luna Lovegood believes in and most people (especially the ever-rational Hermione) don't. Now we know that Luna is a bit ... odd, and believes in a lot of nonsense; but on the other hand, Hermione's pooh-poohing isn't always to be believed either - Divination, for instance, is a real thing in the Potterverse.  Is it ever established for sure, in canon, in-universe, whether or not Crumple-Horned Snorkacks exist? Why did the First Order do this at the cantina? In The Force Awakens, after the First Order are alerted to BB-8, Rey, and Finn's presence at the cantina, an aerial bombardment of the compound begins. They also deploy ground troops.  Wouldn't it have been better to not have an aerial bombardment and simply have the troops surround the cantina, keeping as many people as possible bottled up inside it while they searched both the interior and surrounding area for BB-8?  Instead of a surgical extraction, the strategy that they chose seemed to create chaos and even risked destroying BB-8.  Perhaps this was a sign of the inexperience and emotionally-charged state of Kylo Ren, but General Hux seemed to have more direct authority over the deployment of troops and fighters.  So what was the strategy behind these tactics? Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$ Is $$\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$$ uniformly convergent on $(0,+\infty)$? Sadly, Weierstrass' criterion nor Cauchy's condition don't seem to work here and I just ran out of ideas. Are delphi variables initialized with a value by default? How to redirect with "www" URL's to without "www" URL's or vice-versa? I am using ASP.NET 2.0 C#. I want to redirect all request for my web app with "www" to without "www"  www.example.com to example.com  Or  example.com to www.example.com  Stackoverflow.com is already doing this, I know there is a premade mechanism in PHP (.htaccess) file. But how to do it in asp.net ?  Thanks How can I install Steam? How can I install and run  on Ubuntu? References in Chapter Titles How to register my unregistered account Possible Duplicate:          I've been using my SO account for couple of days, but I am not registered and I do not want to lose all my questions. How can I register and keep my questions from my unregistered account? i.i.d. random variables uniform distribution Why is Android refusing to resolve DNS records pointing to internal IP addresses?