A naive user of RSA has announced the public key $n = 2903239, e = 5$. Eve has worked out that $n = 1237×2347$. Verify that the public key is valid and explain why the private key is $d = 2319725$. [Calculators are not required.]  This question comes from a mock exam that I am trying to solve for tomorrow.  I attach my working out:  $n = p\;q = (1237)(2347) = 2903239$  $\varphi(n) = (1237-1)(2347-1) = 1236(2346) = 2899656$  $d\;e \bmod \varphi(n) = 1$  $e = 5$  $5\;d \bmod 2899656 = 1$  Applying the Euclidean algorithm:  $5\;x + 2899656\;y = 1$  $2899656 = 5(579931)+1$   The public key part: $(e,n) = (5, 2903239)$ The private key part: $(d,n) = (2319725,1)$   I do not understand how the private key is calculated, nor how to do this with a calculator. Any help would be welcome.  EDIT: $$\varphi (n) = (1237-1)(2347-1)= 2899656 \neq 2903239$$  de mod (phi(n)) = 1  5d mod 2903239 = 1   5x + 2903239y = 1  2903239 = 5(580647)+4  5 = 4(1) + 1  1 = 5 - 4(1)  1 = 5 - (2903239 - 5(580647)  1 = 5 - 2903239 + 5(580647)  1 = 5(580648) - 1(2903239)  I am still unsure of how to obtain the private key value from this.  2903239 - 5860648 = 2322591  This value is not the same as the desired value of d, d = 2319725.
When given $p = 5, q = 11, N = 55$ and $e = 17$, I'm trying to compute the RSA private key $d$.  I can calculate $\varphi(N) = 40$, but my lecturer then says to use the extended Euclidean algorithm to compute $d$. That's where I get stuck.    Here's my work so far:  First I use the Euclid algorithm to calculate:  40 = 2(17) + 6  17 = 2(6) + 5 6 = 1(5) + 1 = gcd   So I know the GCD is 1. Applying the 'extended' section of the algorithm:  6 = 40-2(17) 5 = 17-2(6) 1 = 6-1(5) 1 = 6-1(17-2(6)) 3(6) = 1 (17) 3(40 - 2(17)) - 1(17) 3(40) - 3(17)   I know the answer is $33$, but I have no idea how to get there using the extended Euclidean algorithm. I can't figure out why I'm getting $3(40) - 3(17)$ when I know the answer should contain $33$.
When to use single quotes, double quotes, and backticks in MySQL Best way to transfer files from Windows to Windows via Internet Please make the multiple comment timer less annoying (non-resetting etc.) As a little feature to prevent comment spam, you can only enter one comment every 15 seconds. That's a very reasonable limitation, since you very rarely have a good reason to write comments that quickly. I've only seen it twice at all, I think, but both times it was extremely annoying.     Only 1 comment allowed per 15 seconds; timer reset.   The reason is that every time you hit the limit, the 15 seconds begin anew. You have no indicator that tells you when you are allowed to comment again, and if you hit enter after just 14 seconds, you're back to zero. Yesterday, I went through four cycles of not quite 15 seconds, counting in my head, before I got a myself a coffee and tried again afterwards.  I suggest that you do one or more of the following (in decreasing order):   Make the counter non-restarting Add a visible countdown Make it clearly visible that you can't comment right now You can actually increase the waiting time, if it is clearly visible and there is no unnerving invisible countdown. Actually, just remove all comment fields after one comment, and tell the user to reload the page. Just please don't have UI elements that look like they would work, but feel like they are trolling you. Resize image in Python without losing EXIF data I need to resize jpg images with Python without losing the original image's EXIF data (metadata about date taken, camera model etc.). All google searches about python and images point to the PIL library which I'm currently using, but doesn't seem to be able to retain the metadata. The code I have so far (using PIL) is this:  img = Image.open('foo.jpg') width,height = 800,600 if img.size[0] &lt; img.size[1]:     width,height = height,width  resized_img = img.resize((width, height), Image.ANTIALIAS) # best down-sizing filter resized_img.save('foo-resized.jpg')   Any ideas? Or other libraries that I could be using? What is the difference between /sbin/nologin and /bin/false? I have often heard it recommended that a user account should be disabled by setting its shell to /bin/false. But, on my existing Linux systems, I see that a great number of existing accounts (all of them service accounts) have a shell of /sbin/nologin instead.  I see from the man page that /sbin/nologin prints a message to the user saying the account is disabled, and then exits. Presumably /bin/false would not print anything.  I also see that /sbin/nologin is listed in /etc/shells, while /bin/false is not.  The man page says that FTP will disable access for users with a shell not listed in /etc/shells and implies that other programs may do the same. Does that mean that somebody could FTP in with an account that has /sbin/nologin as its shell?  What is the difference here? Which one of these should I use to disable a user account, and in what circumstances? What other effects does a listing in /etc/shells have? Git for beginners: The definitive practical guide Ok, after seeing , I have decided to skip to the end and go with .  So what I need is a beginner's practical guide to Git.  "Beginner" being defined as someone who knows how to handle their compiler, understands to some level what a  is, and has touched source control without understanding it very well.  "Practical" being defined as this person doesn't want to get into great detail regarding what Git is doing in the background, and doesn't even care (or know) that it's distributed.  Your answers might hint at the possibilities, but try to aim for the beginner that wants to keep a 'main' repository on a 'server' which is backed up and secure, and treat their local repository as merely a 'client' resource.  So:  Installation/Setup    How do you set up Git?  Try to cover Linux, Windows, Mac, think 'client/server' mindset.         Working with the code          How do you handle binary files (visio docs, for instance, or compiler environments)? How do you merge files changed at the "same time"?    Tagging, branching, releases, baselines    How do you pull a particular 'release'?   How do you resolve conflicts and complete the merge? How do you merge parts of one branch into another branch?        Other   Describe and link to a good GUI, IDE plugin, etc. that makes Git a non-command line resource, but please list its limitations as well as its good.    - Cross platform, included with Git  - Cross platform history viewer, included with Git  - Mac OS X  - Mac OS X history viewer  - Cross platform, commercial, beta  - console GUI for Linux  - GUI for Windows, Linux  - package for Windows, includes friendly GUI  Any other common tasks a beginner should know?     How do I work effectively with a subversion repository set as my source control source?   Other Git beginner's references                 Delving into Git     (and )    I will go through the entries from time to time and 'tidy' them up so they have a consistent look/feel and it's easy to scan the list - feel free to follow a simple "header - brief explanation - list of instructions - gotchas and extra info" template.  I'll also link to the entries from the bullet list above so it's easy to find them later. I just moved to a new computer: Windows 10 with XAMPP. As far as I know I set everything up the same as it was on my old Windows 7 computer. But now, for some reason, much of the time when I run drush cc all or run update.php, the database gets corrupted. Most frequently, some cache tables' *.idb files (tablespaces) are deleted from my mysql directory, which makes those tables appear as "in use" in phpMyAdmin and prevents them from being edited or emptied. They are always cache tables and never tables that actually get modified by my update hooks. Restoring the database is the only way to fix it then. This is a mature site that I've been working on for a long time, and have never seen this until the new computer. What's happening here?  A sample error message when using update.php, caused by a missing *.idb file:  PDOException: SQLSTATE[HY000]: General error: 1812 Tablespace is missing for table '(null)': DELETE FROM {cache_field} WHERE (cid = :db_condition_placeholder_0) ; Array ( [:db_condition_placeholder_0] =&gt; field:message_type:6 ) in cache_clear_all() (line 168 of C:\&lt;path&gt;\includes\cache.inc).   My most recent drush cc all error message, which Google has never even heard of, was:  exception 'PDOException' with message 'SQLSTATE[HY000]: General      [error] error: 1030 Got error -1 "Internal error &lt; 0 (Not system error)" from storage engine InnoDB' How can I disable the purple splash screen at boot? How can I disable the purple "Ubuntu" splash screen that displays at boot before the login screen has loaded? I'd prefer to just see plain text scroll by. 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Cam I have two GFCIs connected to one double gang box in my laundry room and if so can I do a single line connection so that they both can work independently?  I have a 12/2 going from the panel through conduit (copper wire) to the double gang box. I want to have each GFCI to run independently without using the load. Why, in case one shuts off the other isn't affected. the double gang box is standard. the device is a Leviton 20 amps. I was told that you can run 12/2 from the panel to the first GFCI black and white. Then connect the second GFCI using a jumper and attaching it to he second GFCI. Is this acceptable by code. we use a washer,dryer in the laundry and the garage heavy machinery. so why should this be a problem running two independent? How to prove that a simple graph having 11 or more vertices or its complement is not planar? $P(X<Y)$ where X and Y are exponential with means $2$ and $1$ How to increase swap space? I have, by default, 250MB of swap space in Ubuntu, and I want to expand it to a larger size. I need 800MB, which I think will be enough to open several applications without having to hit the current limit of swap. I hope someone can help me. How do they decide Blu-ray/DVD release date? I think my question is different from .  Some movies' productions release Blu-ray/DVD so early after theatrical release, others will take time. How do they decide for the Blu-ray/DVD release date? Is it safe to have laptop turned on 24/7? I have an old HP dv7-7210sp laptop and I want to use it as a server. Is it safe to have it turned on 24/7? The server will be used with Nextcloud to backup my data.  Should I remove the battery from the laptop or keep it as a backup power source?  Also, is it safe to run HDD 24/7 or should I enable APM so it spins down after some time of inactivity?  Can the laptop burn if I leave it running? What is the difference between confidence intervals and hypothesis testing? I have read about   with some commentators suggesting that hypothesis testing should not be used. Some commentators suggest that confidence intervals should be used instead.    What is the difference between confidence intervals and hypothesis testing? Explanation with reference and examples would be appreciated. How can I install a package without installing some dependencies? I'm trying to install the package LaTeXila, and the output looks like this:  $ sudo apt-get install latexila --no-install-recommends Reading package lists... Done Building dependency tree        Reading state information... Done The following extra packages will be installed:   latexila-data latexmk luatex tex-common texlive-base texlive-binaries   texlive-common texlive-doc-base texlive-latex-base Suggested packages:   rubber texlive-latex-extra debhelper Recommended packages:   texlive texlive-latex-recommended texlive-luatex lmodern   texlive-latex-base-doc The following NEW packages will be installed:   latexila latexila-data latexmk luatex tex-common texlive-base   texlive-binaries texlive-common texlive-doc-base texlive-latex-base 0 upgraded, 10 newly installed, 0 to remove and 0 not upgraded. Need to get 29.3 MB of archives. After this operation, 74.5 MB of additional disk space will be used. Do you want to continue [Y/n]?   I don't want to install the texlive packages. I've installed texlive manually from . Any suggestions? Realtek RTL8723be doesn't have good reception Only when I'm closer to the router, it shows any signal, but when I'm just little far from it, it is not showing wifi routers signals.