Extended Euclidean Algorithm in RSA
Calculating RSA private exponent when given public exponent and the modulus factors using extended euclid
How to prove that the center of the dihedral group $D_{2n}$ is $\{1,r^{n}\}$ and the center of $D_{2n-1}$ is $\{1\}$?  I don't know how to prove it in this general case. How old is Chewbacca, anyway? Do Wookiees get gray fur when they are old? How t show $f=g$ almost everywhere I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$? Short story about dead soldiers bodies being reused How to open and repair an m4v or mp4 video file? Yesterday I was filming a scene with my phone but suddenly the application crashed and when I try to open the m4v generated it says that is corrupted.  I have downloaded the video files (around 36MB) on my PC and I am trying to open and repair it. Can you suggest me a way to do it?  FFMPEG info  As suggested in comments I try check what FFMPEG says me about that file with this command  ffmpeg.exe -i VID_20120425_144739.m4v -c:v copy -c:a copy out.mp4 2&gt; log.txt   Here it is the result:  ffmpeg version N-40126-ga4b58fd Copyright (c) 2000-2012 the FFmpeg developers   built on Apr 26 2012 03:29:50 with gcc 4.6.3   configuration: --enable-gpl --enable-version3 --disable-w32threads --enable-runtime-cpudetect --enable-avisynth --enable-bzlib --enable-frei0r --enable-libass --enable-libcelt --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libfreetype --enable-libgsm --enable-libmp3lame --enable-libnut --enable-libopenjpeg --enable-librtmp --enable-libschroedinger --enable-libspeex --enable-libtheora --enable-libutvideo --enable-libvo-aacenc --enable-libvo-amrwbenc --enable-libvorbis --enable-libvpx --enable-libx264 --enable-libxavs --enable-libxvid --enable-zlib   libavutil      51. 47.100 / 51. 47.100   libavcodec     54. 15.100 / 54. 15.100   libavformat    54.  3.100 / 54.  3.100   libavdevice    53.  4.100 / 53.  4.100   libavfilter     2. 72.100 /  2. 72.100   libswscale      2.  1.100 /  2.  1.100   libswresample   0. 11.100 /  0. 11.100   libpostproc    52.  0.100 / 52.  0.100 [mov,mp4,m4a,3gp,3g2,mj2 @ 003fc940] moov atom not found VID_20120425_144739.m4v: Invalid data found when processing input   Latest two lines are displayed in red. What are Thumbs.db files for? How can I prevent them from being created? On the websites, whenever the OP comments on an answer, or on his question, his name is highlighted. This is a handy feature because you can easily tell whether the comment is from the OP or not.   But on the Android mobile app (don't know about iOS),  this feature is not there. Can we have it please!? How to make terminal autocomplete when there are several files/directory? If I have several directories, like:  afoo abar   sometimes my terminal will refuse autocomplete when I press tab (e.g. "cd a" then tab), and print the list of directories instead. Sometimes it even throws a noisy, annoying sound. Any idea how to make it autocomplete in cases like this? E.g it can show abar first, and then afoo if I press tab again. I saw this is the case in windows, or some applciation in Ubuntu Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence I've been reading the simple parts of Thomas Jech's book on the Axiom of Choice and came across the following proof on page 141. The proof assumes a mathematical model without the axiom of choice.     Lemma. $X$ is D-finite if and only if $X$ does not have a countable subset.       Theorem. There is a set $S$ of real numbers and a real number $a \not \in S$ such that a is in the closure of $S$ but there is no sequence $(x_n)^{\infty}_{n=0} \subset S$ such that $(x_n)^{\infty}_{n=0} \longrightarrow a$.       Proof. Let $D$ be a D-finite infinite set of reals. We claim that the set $D$ must have an accumulation point. To prove this claim suppose that all $d \in D$ are not accumulation points, then let $\{I_n:n=0,1,...\}$ be a fixed enumeration of open intervals with rational endpoints. Assign the least $n$ such that $I_n \cap D={d}$ to each $d \in D$. This makes $D$ countable and by the above lemma gives us our contradiction. So $D$ has an accumulation point $a$. Let $S=D \setminus\{a\}$ and since $S$ is D-finite, every convergent sequence in $S$ is eventually constant.   Could somebody explain this proof? Why is the last sentence true/ Why does this mean every convergent sequence is eventually constant?  I think the following theorem is important     Theorem. There is a model of ZF which has an infinite set of real numbers without a countable subset Attacks of the MAC construction $\mathcal{H}(m\mathbin\|k)$ for common hashes $\mathcal{H}$? I have uploaded an excel sheet into static resource of my environment. I have it as a demo for my product how to create a excel sheet for import records into sf. Can any body guide me how can i provide link on the VF page so that user can download the record at single click.I want to into a managed package and want users to be able to click the link on the Vf page to download. Right now i have my demo excel sheet in static resource. I am open if you have any other ideas to get the process done. How do I get an up/parent button in Nautilus, without using breadcrumbs? Suppose there are two face down cards each with a positive real number and with one twice the other. Each card has value equal to its number. You are given one of the cards (with value $x$) and after you have seen it, the dealer offers you an opportunity to swap without anyone having looked at the other card.  If you choose to swap, your expected value should be the same, as you still have a $50\%$ chance of getting the higher card and $50\%$ of getting the lower card.  However, the other card has a $50\%$ chance of being $0.5x$ and a $50\%$ chance of being $2x$. If we keep the card, our expected value is $x$, while if we swap it, then our expected value is: $$0.5(0.5x)+0.5(2x)=1.25x$$ so it seems like it is better to swap. Can anyone explain this apparent contradiction? What is tail recursion? Whilst starting to learn lisp, I've come across the term tail-recursive. What does it mean exactly? For a physics major, what are the best books/references on Greens functions for self-studying?  My mathematical background is on the level of Mathematical Methods in the physical sciences by Mary Boas. why does OSX add extra '._' when I tar a directory? I'd just like to know why if I "tar -czf" a file/directory, osx adds a:  ._  for each file? I see these when I untar in linux. Or when I work with the uncompressed project in eclipse as it doesn't like them at all. I use 10.7.5. Not booting from USB or CD (SYSLINUX Message) I am trying to install linux on my laptop, a Toshiba Satellite C6550-S5200. I did it once but something happened so I removed it then I had to destroy all data on hard drive so now I have nothing on it. Well I got a iso file burned to a CD and to a flash drive. With the flash drive I get.   SYSLINUX 4.06 EDD 4.06-pre7 Copyright (C) 1994-2012 H. Peter Anvin et al  With the CD it will start booting it but somewhere loading it up, the dots turn all orange and stay that way and my CD drive turns quiet.  Oh and some more info the images work because I tried loading them up on another pc and it worked just fine.  I manage to get the CD to boot I just had to let me pc boot up first then insert the CD and have it boot the CD then. Once I get done installing ubuntu it works fine but I have to leave the PC on 24/7 for if I turn it off the PC will freeze 5-10 seconds after booting back up no matter how I install it. How does one prove that every finite group is isomorphic to a subgroup of an alternating group? Badge overflow on users with too many badges When a user has &quot;too much&quot; reputation and &quot;too many&quot; badges, the design of the user card breaks:    The badge counters overflowing to another line. Can anything be done about this? For example, expanding the rep and badges to their own lines:  NameRepBadges