Proving something using Pigeonhole Principle
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
Calculate Time Remaining For files within a specific folder, I would like vim to never touch "modified" timestamp at all.  The background is that I use  for blogging, which uses plain text files in ~/bloxsom as source of all articles.  The article date (and therefore order of appearence) is based on modification date of the text file. I don't want article pop up like if it's new whenever I just fix a typo. (I do lots of them... :D)  So far, vim changes timestamp and the original stamp is lost forever.  This is OK and I want to keep it that way for most of files on the system.  But I don't want that for the blog files - I can always touch the file if I need.  Any ideas on how to tweak vim into this behavior? How to select the most recent set of dated records from a mysql table Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$ Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$.   I was thinking among the lines of:  Since $a$ and $b$ are coprime numbers, $\gcd(a,b)=1$. Then there exist integers $x$ and $y$ such that, $ax+by=1$.   Then, $a=(1-by)/x$, $b=(1-ax)/y$  So if I write $2^a+1$ as:  $2^{(1-by)/x}+1$  Then can I say that the above expression is equivalent to 0 (mod 3)? Most people with a degree in CS will certainly know what . It helps us to measure how well an algorithm scales.   But I'm curious, how do you calculate or approximate the complexity of your algorithms? AES Mix Column Transformation Section 3.4.3 "The MixColumns Step"(page 39) of , it states     The columns of the state are considered as polynomials over   $\operatorname{GF}(2^8)$ and multiplied modulo $x^4 + 1$ with a fixed polynomial $c(x)$.      The polynomial $c(x)$ is given by   $c(x) = \mathtt{03} \cdot x^3 + \mathtt{01} \cdot x^2 + \mathtt{01} \cdot x + \mathtt{02}$      Let $b(x) \equiv c(x) \cdot a(x) \pmod{x^4 + 1}$. Then         How this polynomial multiplication modulo $x^4+1$ is converted to Matrix Multiplication? Keyboard Shortcuts no longer working on GNOME 3.4.1 How to partition a list in a specific way How do I completly remove XP from my pc. I currently have a dual boot with XP and Windows 7. Since installing Windows 7, I have never used XP. Can I remove it without causing problems with Windows 7? How to kill the process using the name of the program instead of PID? I started my Python program in the background using nohup as mentioned below -   nohup zook.py &amp;   Now I am trying to kill this process so I did the ps command as mentioned below  root@phxdbx1145:/home/david/zook# ps ax | grep zook.py 16352 pts/6    S+     0:00 grep --color=auto zook.py   But somehow, everytime its PID getting changed, I don't know why. Whenever I do like this -   kill -9 16352   It always say, No Such Process.  And when I do px command again, I see that PID got changed automatically..  So I am not sure how do I kill this process?  Is there any way I can kill the process with the name somehow?  UPDATE:-  This is what I am getting. I did pkill -9 zook.py and then I did ps command as mentioned below and it is shwoing zook.py constantly?  root@dbx1145:/home/david/zook# pkill -9 zook.py  root@dbx1145:/home/david/zook# ps ax | grep zook.py 23870 pts/6    S+     0:00 grep --color=auto zook.py  root@dbx1145:/home/david/zook# ps ax | grep zook.py 23872 pts/6    S+     0:00 grep --color=auto zook.py  root@dbx1145:/home/david/zook# ps ax | grep zook.py 23874 pts/6    S+     0:00 grep --color=auto zook.py  root@dbx1145:/home/david/zook# ps ax | grep zook.py 23876 pts/6    S+     0:00 grep --color=auto zook.py It said  that:     [....] Rijndael can be specified with block and key sizes in any multiple of 32 bits, with a minimum of 128 bits. The blocksize has a maximum of 256 bits, but the keysize has no theoretical maximum.   How would the key schedule look for these other key sizes, like a 136-bit key? What can be said about the convergence on $|z|=1$? I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. How can I reset my Ability Points? I'm also curious about being able to reset my points, should I wish to change my ability configuration later.  So far (10h-ish) I've only seen one way, which is a potion sold by Kiera Metz for 1000g. However she's no longer available as a store, due to a story choice, so I'm not sure where else I could buy this potion.  Where might I buy this potion, and is it the only way to reset your ability points? At school, I really struggled to understand the concept of imaginary numbers.  My teacher told us that an imaginary number is a number that has something to do with the square root of $-1$.  When I tried to calculate the square root of $-1$ on my calculator, it gave me an error.  To this day I still do not understand imaginary numbers.  It makes no sense to me at all.  Is there someone here who totally gets it and can explain it?  Why is the concept even useful? I'm drawing a scene where the camera freely moves about the universe.  The camera class keeps track of the view (or look at) point, the position of the camera, and the up vector.  These vectors/points are then passed into gluLookAt.    Pan and zoom are nearly trivial to implement.  However, I'm finding rotation about the look at point to be much more of an issue.  I want to write a function Camera.rotate that takes 2 angles, one that rotates up/down and one that rotates left/right along an imaginary sphere that is centered about the look at point.  Is there an easy way to do this?  I've (briefly) read about quaternions, but I wanted to see if there was an easier solution given the relatively simple construction of my scene. Series about being that could change sex and age - "The Morph*" I'm trying to remember information about a series of three books I read in the early 1980's (first book could have been published in the 1970's). The book featured a character who was a scientific creation of some sort. It was (initially, I believe) an assassin, and had the ultimate getaway scheme; with effort, it could change its body, becoming about 10 years younger and switching sex. It changed 4 or 5 times in the first book, coming down from a senior citizen to someone in their teens or twenties; in the second and third books, it changed once per book (by the last book, it was a child or a young teenager).  The first book was title something like "The Morph..." where whatever the word was that started with "Morph" was this creature. No recollection of the author's name, or the titles of the other two books.  I think the cover of the first book was predominantly yellow, with black silhouettes representing the character at the four ages seen in the book, and a black title. And/or, the book might have been published by DAW (all their books at the time had yellow spines with black letters). How to correctly label an included PDF? I have this:  \label{appendix:b} \includepdf[scale=0.8,pages=1,pagecommand=\chapter{interview}]{interview/interview} \includepdf[scale=0.8,pages=2-,pagecommand={}]{interview/interview} \label{appendix:bslut}   And I'm calling it with cleveref:  \cpagerefrange{appendix:b}{appendix:bslut}   The problem is that I get the wrong page number for the last page -- it adds a page. What should be "pages 1-5" is instead "pages 1-6". I have Googled this like a madman, and I can't figure out what to do. I hope some of the superstars here can help! I have cleveref after hyperref, as recommended...  EDIT: As requested, I tried to make an MWE, but for some reason it gives me:  LaTeX Warning: Reference `appendix:bslut' on page 1 undefined on input line 7.   Here it is, though. "multipage" should be a PDF spanning several pages.  \documentclass{memoir} \usepackage{pdfpages} \usepackage{hyperref} \usepackage{cleveref} \begin{document} \chapter{Foo} Foo\cpagerefrange{appendix:b}{appendix:bslut}.  \chapter{Bar} \label{appendix:b} \includepdf[scale=0.8,pages=1,pagecommand=\chapter{Multipage}]{multipage} \includepdf[scale=0.8,pages=2-,pagecommand={}]{multipage} \label{appendix:bslut}  \end{document} My wife is an Indian national with an Indian passport. She holds an indefinite leave to remain in the UK (permanent residence card). Does she need to apply for a Schengen visa before travelling to France or any other Schengen countries? Correct ssh config file settings to tunnel to a 3rd machine I'm trying to tunnel to a server via a bridge server. So far, I've been able to get it working from the command shell properly using the following command:  ssh -A -t bridge_userid@bridgemachine.com ssh -A remote_userid@remoteserver.com   But I've been trying to wrap this into my ~/.ssh/config file and I have troubles. I've tried:  Host axp   User          remote_userid   HostName      remoteserver.com   IdentityFile  ~/.ssh/id_rsa.eric   ProxyCommand ssh -A -t bridge_userid@bridge_userid.com ssh -A remote_userid@%h   But when I do, I get the following error message from remoteserver.com and I'm not sure what is causing it:     ksh: SSH-2.0-OpenSSH_6.8^M:  not found   I know that when I log into remoteserver.com , my shell is /usr/bin/ksh.  I've tried to add path arguments to the ssh commands in the config file, but it made no difference.  Any ideas what it can be? Intuition behind using complementary CDF to compute expectation for nonnegative random variables I've read the proof for why $\int_0^\infty P(X &gt;x)dx=E[X]$ for nonnegative random variables (located ) and understand its mechanics, but I'm having trouble understanding the intuition behind this formula or why it should be the case at all. Does anyone have any insight on this? I bet I'm missing something obvious.