Reading about AKS primality test I've encountered the expression $(x+1)^n \equiv x^n+1 \mod{(n, x^r-1)}$. What does the notation $x\equiv y\mod{(r,s)}$ mean in general? Is it simply $x \equiv y \pmod r\pmod s$?
Where does a layman go to get a basic understanding of AKS primality testing. I am not talking about the optimal choice of $r$ (which I am told is the hardcore number-theoretic part of the algorithm). I mean basic things, like what does $\bmod(n, x^r-1)$ mean (how can something be mod two things?) And what does binomial expansion have to do with anything?  I can't find anything in Wikipedia that is appropriate for my level.
Why does everything spin? The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons.  Where has all the angular momentum come from? Why is it so natural?  I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate in 3d? What implications would this have?   And what about spacetime how does all the spinning effect?  This has always been avoided in all lectures and classes I ever went to. Can I transfer or sync purchased as well as non-purchased songs from my iPhone to my computer? Can I invoke Google to check my robots.txt? I read the answers in this question, but they still leave my question open:   I didn't find a way in the Google Webmaster Tools to invoke a re-download of my robots.txt.  Through some error, my robots.txt was replaced with:  User-agent: * Disallow: /   And now all my content was removed from Google search results.  Obviously, I'm interested in correcting this as soon as possible. I already replaced the robots.txt, but I can't find a way to make Google update the cached version. How to tell the order of a Feynman diagram? How can we know the order of a Feynman diagram just from the pictorial representation?  Is it the number of vertices divided by 2?  For example, I know that electnro-positron annihilaiton is first order:   So what's the order of, for instance, a radiative penguin diagram (below) ? List of Stored Procedure from Table I have a huge database with 100's of tables and stored procedures. Using SQL Server 2005, how can I get a list of stored procedures that are doing an insert or update operation on a given table. Executing a certain action for all elements in an Enumerable Should my first trip be to the country which issued my Schengen Visa? I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. I'm trying to approximate the computer's write speed using dd:  dd if=/dev/urandom of=/dev/null bs=1K count=10000   which gives the following output  10000+0 records in 10000+0 records out 10240000 bytes (10 MB) copied, 0.746313 s, 13.7 MB/s   How can I get the '13.7 MB/s' into a bash variable? I've tried piping the output from dd to progs like awk, sed and grep to no avail.  Ultimately, I'm calling this via os.system(...) from within a python script. If anyone knows of a more direct way to get a similar result inside python I'd be interested in that also. I'm trying to predict how long a file copy will take, based on the file size.  Any help would be greatly appreciated. What's a big-vocabulary word for someone with a big vocabulary?  I'd like to say I'm looking for a "_____". What's the difference about /t̬/ and /d/? Why does this Excel file keep asking to save? If I attempt to change my password to nothing by opening "User Accounts", the "Change" button remains greyed out:    How do I change my password to be empty? I know you can set Ubuntu to automatically log you in, but I want my password to be empty, I never want to type in a password to authenticate myself as that user.  I know that there are reasons why this might not be a good idea, but I want to know if it is even possible. I'm using Ubuntu 12.10. I need to end my visa waiver period when leaving States to Canada so that I don't exceed the period of 90 days. But form I-94 is no longer a physical card, it's only online.  How do I know or ensure that it will be terminated and will not continue counting the days once I leave to Canada? Word for romantic partner you are living with but not married to computing the orbits for a group action Let $G$ be the Galois group of a field with nine elements over its subfield with three elements. Then the number of orbits for the action of $G$ on the fields with nine elements is   3 5 6 9   I have no idea how to compute the numbers of orbits for a group action. Anyone please help me. Thanks. Why doesn't my flash fire from the hot shoe trigger? I have a Yongnuo YN-560 III and a pair of RF-603II (C3) triggers. I have a Canon Rebel T5i.   I put one trigger on the hot shoe.  When this trigger is in TX mode I get a blue comm light and I can fire a test flash using the large test button on the trigger. But when I press the shutter button to take a picture, there's no flash.  The trigger and flash are on Channel 1. The trigger on the hot shoe is set to TRX. TX is fine, TRX gives me no flash. The flash and camera are in M mode.  I don't have a trigger on the flash because the Mark III has a built-in trigger The problem seems to be the camera.  The trigger can talk to the flash but the camera is not sending a flash command through the trigger in the hot shoe to the flash.  Grateful for anything you could suggest. How can I copy a custom Dictionary on Word 2000? Can I programmatically open the devtools from a Google Chrome extension? As a result of  myself, the need arose to track other Stack Overflow-based research. The following is an attempt to list the academic papers mentioning Stack Overflow/Exchange or using Stack Exchange data. This also includes the works mentioned in  that started the trend, as well as two other questions on meta, , and . If you know of papers that are not listed, please edit the answer directly. I realised it might be useful to have all the BibTeX entries in a single file, so I started .