How do I prove that $X^{p^n}-X$ is the product of all monic irreducible polynomials of degree dividing $n$?
Product of all monic irreducibles with degree dividing $n$ in $\mathbb{F}_{q}$?
using Ajax with 3 consecutive drop down lists depending on eachother Can I adjust starting point when using ListPlot? Could a ship warp into Borg cube and destroy it? During the Wolf-359 incident, 39 starships were destroyed, and 11,000 people were killed or assimilated.  Why didn’t one of the smaller ships warp into that one Borg cube? Doesn’t warping into it destroy anything?  Even if it just warps through without touching, one could program the navicom to self destruct while the ship is in the middle of Borg cube. How to find the inverse modulo $m$? For example: $$7x \equiv 1 \pmod{31} $$ In this example, the modular inverse of $7$ with respect to $31$ is $9$. How can we find out that $9$? What are the steps that I need to do? Update If I have a general modulo equation: $$5x + 1 \equiv 2 \pmod{6}$$ What is the fastest way to solve it? My initial thought was: $$5x + 1 \equiv 2 \pmod{6}$$ $$\Leftrightarrow 5x + 1 - 1\equiv 2 - 1 \pmod{6}$$ $$\Leftrightarrow 5x \equiv 1 \pmod{6}$$ Then solve for the inverse of $5$ modulo 6. Is it a right approach? Thanks. Autoexpand UITextView height dynamically in ios I'm using the caption package.  In the List-Of-Figures I get only the numbers, but I also want to have the prefix. It currently looks like that:     List of Figures   1 Caption of Figure 1........1   2 Caption of Figure 2........9     And I want it to look like:     List of Figures   Figure 1: Caption of Figure 1...1   Figure 2: Caption of Figure 2...9     The same format is already used for the captions themselves. On Takodana,      the main characters and various bar patrons can see the planet Hosnian Prime being destroyed by Starkiller Base with their (respective) naked eyes. How did they see this? Is the Hosnian system close enough to see? If it's not very close and they could just see the explosion, how did the light from it reach them so quickly? alias multi commands as one alias I made an alias for youtube-dl  with some options  like that  yd="youtube-dl -cit -f 18"   so I can download it like   yd URL   I want to modify it to show only the two lines from the output using   grep -e "Downloading video #" -e ETA  I can make it in two aliases using the |   but is there a way to make it one alias Rename files in directory according to name of directory I am trying to rename a bunch of files according to the names of their directory in Linux, SSH.  I have a directory called XYZ01smith. In it are four files called smith_5*.I need to add prefix XYZ01 to these files. But, the next directory is called XYZ02perry. In it are four files called perry_3*. I need to add the prefix XYZ02 to these files.  I have a loop to do this per directory:  for i in smith_5*;     do mv ${i} XYZ01${i}; done    But I have 50 directories (XYZ01name to XYZ50name), so I would rather be able to do this with one script for all 50. I am sure this should be possible, but I do not know how. Windows 10 changes UEFI boot order every time I have an HP 500-413nl (a desktop) and Windows 10 keeps changing the boot order in UEFI/BIOS every time, so that if I want to boot Ubuntu 16.10 (64-bit) I always have to press F10, thus entering the BIOS setup and changing boot order…  Is there a workaround for my PC? What should I do? I'm a little desperate.  P.S.: I have already disabled "Secure boot" and "Fast/quick boot" in the BIOS and "Fast startup" in Windows options / Control panel. Why doesn't hydrogen gas exist in Earth's atmosphere? How can I change the default location for bluetooth file transfers? I have an Android 2.3 device (Samsung Galaxy Y Duos, S6102) and want all files that I receive via bluetooth to save to my SD card.  How can I do that? I have a featureclass in an Esri file geodatabase. When I edit the features using the editor in ArcMap, and I delete most of my features and keeping only the ones in the middle, the zoom to layer command doesn't work as expected. Instead of zooming to the extent of the features remaining in the feature class, the extent will be the former one (containing all deleted features). When reviewing the extent values in the properties dialog for the feature class, I can clearly see the old values. So the edit session doesn't seem to alter the full extent values.  Is there a way to recalculate these values?  I am pretty sure that this problem should occur to everyone editing features in ArcMap... Often floats may land quite a bit later in the document than the point they are created, sometimes after a section break.  Is there a way to force a new section to start on a new page, after any unplaced floats? 'Good' review audits can be misleading I have noticed a couple of kinds of behavior that seem to crop up in the SO community, and it really seems to artificially boost reputation. There may not be a solution (or it may not be a problem!) but here are some thoughts.  The first is the fact that "celebrity" users, or users with lots of reputation, are treated significantly better than others. Take Joel Spolsky's most recent question:    It was closed, opened, closed, and re-opened. And the question has earned Joel - what - 1030 reputation 103 votes, and lots of reputation! Wow! I'm not saying that Joel's question is a bad one. But lets compare to other questions that one might consider to be in the same equivalence class - easily answerable, specific questions, short questions:   (5 votes)   (5 votes)  If you look at the , I can hardly find any which are specific technical questions. So that Joel's question was so upvoted could only mean that:   It was upvoted based on his celebrity People have been interpreting the questions as a sort of zen-like wakeup call, designed to get people talking and thinking about they way they vote.   I do not mean any disrespect toward Joel, and again, I think his question was a good one. This post isn't about Joel! But the boost in reputation did not (imho) mean "Joel is really good at programming, and he has earned my trust as someone knowledgeable about computers." It may be true that Joel is a proficient computer expert, but not based on the merit of that one question.  Which leads me to an example about myself. I recently gave  (130 reputation) to a question about PHP's image-creating libraries. I am very appreciative of the community's support for my answer - an answer which I believe was well-thought and that I put effort into.  At the same time I can't look someone and tell them, with a straight face, that my reputation is a great reflection of my computer-related knowledge. Billions of people on the net have created tutorials for PHP's GD image library - I just happened to be the person to post a few of them. Heck if I know why it got 13 votes! (oh, but please don't downvote it!!)  SO is built by the community - so the community absolutely gets to decide what questions are important, and how they choose to dispense reputation. But in practice, I feel like peoples' reputation would be much lower if the community were more discriminating about the way they voted.  So: am I totally off base here? Is this even something that can be corrected with a different reputation algorithm? Or am I the only one who sees this as a detriment to the SO community?  (And, to be completely clear, I do not intend for this to be an ad hominem, and I am not jealous about not having a higher reputation. But I do take reputation with a grain of salt, in part for these reasons, and I thought I'd bring it up! It is meta, after all!) There are two Java Web Start tags:  : x 239 : x 320   Both tags refer to the same technology  refers to  both wiki point to  all questions tagged with  clearly relate to Java Web Start   I suggest they be merged into  (which appears in the auto-complete list if one types "webstart" in the Tags box when asking a new question). Is a Squib a Muggle? ‘And what on earth’s a Squib?’ said Harry.   To his surprise, Ron stifled a snigger.   ‘Well – it’s not funny really – but as it’s Filch ...’ he said. ‘A Squib is someone who was born into a wizarding family but hasn’t got any magic powers. Kind of the opposite of Muggle-born wizards, but Squibs are quite unusual. If Filch’s trying to learn magic from a Kwikspell course, I reckon he must be a Squib. It would explain a lot. Like why he hates students so much.’ Ron gave a satisfied smile. ‘He’s bitter.’   Chamber of Secrets - pages 110-111 - British Hardcover   If a Squib is 'kind of the opposite of a Muggle-born wizards' wouldn't that make a Squib more Muggle than wizard? Does a Muggle strictly have to be born to Muggle parents to be considered a Muggle, or can the lack of magic render a person, even of wizarding parentage, a Muggle?  Hermione can say in all truthfulness that she is a 'Muggle-born witch.' The nickname (albeit derogatory) for a Muggle-born is 'Mudblood.' Filch can say in all truthfulness that he is a 'wizarding-born non-magic person,' which, according to Hagrid is a Muggle.  'Squib' may be derogatory in the same way as 'Mudblood' is. Neville laments his family thought he was a Squib when he showed no magical tendencies as a child; the Longbottoms were so rattled at the thought of Neville being a Squib that they, among other things, threw him out a second-story window to see if he would bounce. So could 'Squib' actually be a derogatory term meaning the opposite of 'Mudblood'? After all, the Ministry doesn't allow Squibs to register as magical beings, and many Squibs are schooled and trained in Muggle professions. Squibs don't get a Hogwarts letter.    Wizards can be born to Muggles. Can Muggles be born to wizards?  ETA 11.22.14: In regard to this question, I was glancing through Philosopher's Stone, and I came across this, that Neville said:     ‘Well, my gran brought me up and she’s a witch,’ said Neville, ‘but the family thought I was all Muggle for ages. My great-uncle Algie kept trying to catch me off my guard and force some magic out of me – he pushed me off the end of Blackpool pier once, I nearly drowned – but nothing happened until I was eight.’   Philosopher's Stone - page 93 - Bloomsbury - chapter seven, The Sorting Hat   Could what Neville says contribute to the theory and/or conclusion that Squibs are, or are not, Muggles? How do we apply what Neville said? Thought Experiment - Poking a stick across a Black Hole's Event Horizon The classical explanation of a black hole says that if you get to close, you reach a point - the event horizon radius - from which you cannot escape even travelling at the speed of light. Then they normally talk about spaghetti.  But here's a thought experiment. What if I have a BH with event horizon radius R such that the gravitational gradient at the event horizon is far too weak for creating pasta. I build a Ring with radius R+x around the BH. Then I lower a pole of length x+d from my ring towards the BH, so that the tip passes beyond the event horizon.  Now what happens when I try to pull the pole back? I have to deal with a large number of files nested inside of directories (one file per directory), resembling something like this:  fred/result.txt john/result.txt mary/result.txt ...   I am currently using the following command to process each of those files:  find . -maxdepth 1 -type d \( ! -name . \) -exec bash -c \"cd '{}' &amp;&amp; processResult result.txt\" \;   I am looking for something I can add into the end of this command that will change the filenames to fred.txt, etc. and then later move the file into the parent directory to eliminate the extra layer of directories.  What would be the best way to do this?