Prove $z = \frac {5^{125 }- 1}{5^{25} - 1} $ is composite.
Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number
Add a UIButton as a subview to a UITabBar What are quarks made of? So atoms are formed from protons and neutrons, which are formed from quarks.  But where do these quarks come from? What makes them? How can I install software or packages without Internet (offline)? Ok, I have to admit, I don't really delve too deep into the semantics of the spatial operators list below, I'm more of a user, I write software to drive the SQL most of the time and don't really think about it too much.  However, I have a situation where a spatial operation I'm doing is going dog slow, on a table that has great indexes on and has never caused a problem before now.  As a result, I'm trying to figure out which of the following is my best bet to use, that will give me the best performance, however, sometimes I find my searches don't return anything when I know they should, and sometimes return stuff when they shouldn't.  SO I'm reaching out, to ask if some one can give me the actual definition, such as criteria to match, fully within enclosing geometry, or within outer ring etc etc of each of the following operations:  Equals(Geom1, Geom2):int Disjoint(Geom1, Geom2):int Touches(Geom1, Geom2):int Within(Geom1, Geom2):int Overlaps(Geom1, Geom2):int Crosses(Geom1, Geom2):int Intersects(Geom1, Geom2):int Contains(Geom1, Geom2):int Relate(Geom1, Geom2):int   If you can give a concrete example of when they will and will not match too, that would be great.  For reference, I'm searching on a table of Linestrings, using a rectangular polygon, rotated to be pointing in the direction of travel (It's part of a traffic managment app)  For further reference, here is a sample of the SQL the app generates to perform a search:  SELECT recordID,AsBinary(geometry) AS geometry,Distance(GeomFromText('POINT(-1.84101 54.85078)',4326), geometry) AS distanceFromGps FROM linegrid WHERE Intersects(GeomFromText('POLYGON ((-1.8413149820810311 54.850782468607292, -1.8409507853094111 54.850952257034713, -1.8408279009723911 54.850864894077496, -1.8411920982612455 54.850695105650068, -1.8413149820810311 54.850782468607292))'), geometry)   You can see in this example I'm using intersects trying the others as mentioned doesn't quite give the results I expect, hence why I'm asking the question.  Please note, I'm not particularly bothered about actual faster/other ways of doing this at the moment, BUT if you do happen to spot a better way do feel free to shout up :-)  For now all I'm mostly trying to understand is the differences between each of the operations.  As for doing it faster/better I intend to open a different question for that at a later date.  For more reference, the Spatial engine this is working against is Spatilite 2.3.0, and I can't upgrade it due to the devices it's running on not having a more up to date build for it (Windows CE)    I'm going to choose mintix'es answer here as that provided a super easy to understand grid and description of all the various operations, which answered my question.  I'm still faced with getting performance on the routines up, but I do now have a few strategies to try on that one, I may still seek advice here from the group with regards to that.  @Vince deserves some credit too, as that white paper is definitely the definitive answer, but it's also quite challenging to read (I had to read through it several times) , for anyone wanting the real I am on these operations The Clementini paper is the way to go, if you need an easy to understand overview while developing solutions however, the FME link should be open in another browser tab. I'm going to mount my 47" LCD above my fireplace. I'm not looking for arguments against this decision. I'm looking for wiring solutions. The diagram below should help explain the situation.   _________________________________________________ |     |     |    | |   |   |   | |    |     |     | |     |     |    | |   |   |   | |    |     |     | |     |     |    | |   |   |   | |    |     |     | |     |     |    | | p |   | m | |    |     |     | |     |     |    | |   |   |   | |    |     |     | |     |     |    #################    |     |     | |     |     |    ##             ##    |     |     | |     |     |    ##             ##    |     |     | |    P|     |    ##             ##  m |     |P C  | |_____|_____|____##_____________##____|_____|_____|    | = stud # = fireplace brick P = existing power outlet C = existing cable outlet p = new power outlet m = new media outlet   Essentially, there is an existing power outlet on either side of the fireplace and a cable outlet on the far right side of the fireplace. I'm intending to put my non-TV media equipment on the right side of the wall and the television above the fireplace. This means I need two things above the fireplace: power and HDMI. I don't want to just run an HDMI cable in the wall. I'd prefer to have some sort of conduit to simplify replacing the cable or having a second (with one of these on each end: ). I only need to drill through two studs that are 6" apart above the right side of the fireplace in order to access the vertical space where I want the other end. For the power, I need to drill through two 6"-spaced studs above the left-side of the fireplace, but then another 2 full-height studs.  There are a couple of caveats:   This is an externally facing wall, which means there's insulation. I'm assuming this will make things more difficult. I'd like to refrain from cutting more holes in the wall than is necessary for the outlets (to reduce drywall damage/repair).   I've considered a couple of options:   Cut the openings for the outlets above the fireplace, and use a flexible drill bit to drill through the studs above the fireplace. This minimizes dry-wall damage, but how difficult is this with insulation in the wall, how can I feed the conduit through those holes, and how would I drill through the full-height studs on the left for power? Cut a wide section of dry-wall (4" high?) from the desired media outlet to the right until reaching the gap above the desired lower outlet. This results in some dry-wall damage, but would allow more control for drilling holes in the studs and running conduit. This still doesn't solve the problem of getting through the full-height stud for the power. For the power, I would need to extend the cut-out two studs further.   What should I do? How to remove white space before reference? What should my Objective-C singleton look like? My singleton accessor method is usually some variant of:  static MyClass *gInstance = NULL;  + (MyClass *)instance {     @synchronized(self)     {         if (gInstance == NULL)             gInstance = [[self alloc] init];     }      return(gInstance); }   What could I be doing to improve this? How does Linux handle multiple consecutive path separators (/home////username///file)? How to use (home) brew install python 3.6.5_1 I am trying to install python 3.6.5_1 using Homebrew by running the following:  $ brew install https://raw.githubusercontent.com/Homebrew/homebrew-core/f2a764ef944b1080be64bd88dca9a1d80130c558/Formula/python.rb   I am getting the following error:  Error: python contains a recursive dependency on itself: python depends on sphinx-doc sphinx-doc depends on python   How do I deal with it? SQL Servers has Traces and XEvents. These are used to capture and analyze what is going on with our SQL Server Instances. Events are stored in the stack for later analysis. For example,  If I decide to monitor any dead lock in the database, I just query the trace file to see the history of deadlock for a period of time. Here is my question:  While events occur, in our example deadlock event, is there a way to get an email notification using msdb.dbo.xp_send_dbmail? Is stopwatch benchmarking acceptable? Does anyone ever use stopwatch benchmarking, or should a performance tool always be used?  Are there any good free tools available for Java?  What tools do you use?  To clarify my concerns, stopwatch benchmarking is subject to error due to operating system scheduling.  On a given run of your program the OS might schedule another process (or several) in the middle of the function you're timing.  In Java, things are even a little bit worse if you're trying to time a threaded application, as the JVM scheduler throws even a little bit more randomness into the mix.  How do you address operating system scheduling when benchmarking? What's the best way of replacing a plug or switch in a house with aluminum wiring? Avoiding the second leg of an international flight - different rates for a return ticket? Possible Duplicate:          I am in the process of booking a flight from LAX - ZUR. I found a flight for approx. 1100 USD. However, if I book that flight and then continue, after a 5 hour layover, onward to SVO, The flight is approx. half of the initial price, and the first leg of the second flight is the exact same flight as the first booking. Assuming I travel light and do not check any baggage, are there any potential issues with this? Seems like a hell of a way to save a good chunk of change. Allow folding/collapsing of certain segments of posts A question with attachments, screenshots and/or long code, makes it vertically long and often difficult to read fast.  It would be nice to have a new kind of format, such as 'hideable', with a graphic button or a '+' / '-' sign, so you can add additional details, visible only on a click. What is the string concatenation operator in Oracle? What is the string concatenation operator in Oracle SQL?    Are there any "interesting" features I should be careful of?    (This seems obvious, but I couldn't find a previous question asking it). Whey I try to run the program Layout Editor (available on ) on Ubuntu 14.04.1 64-bit LTS I get the following output in the terminal:  $ layout layout: /usr/lib/x86_64-linux-gnu/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by layout)   I tried the command strings on /usr/lib/x86_64-linux-gnu/libstdc++.so.6 as following and here is the input and the output:  $ strings /usr/lib/x86_64-linux-gnu/libstdc++.so.6 | grep GLIBCXX GLIBCXX_3.4 GLIBCXX_3.4.1 GLIBCXX_3.4.2 GLIBCXX_3.4.3 GLIBCXX_3.4.4 GLIBCXX_3.4.5 GLIBCXX_3.4.6 GLIBCXX_3.4.7 GLIBCXX_3.4.8 GLIBCXX_3.4.9 GLIBCXX_3.4.10 GLIBCXX_3.4.11 GLIBCXX_3.4.12 GLIBCXX_3.4.13 GLIBCXX_3.4.14 GLIBCXX_3.4.15 GLIBCXX_3.4.16 GLIBCXX_3.4.17 GLIBCXX_3.4.18 GLIBCXX_3.4.19 GLIBCXX_DEBUG_MESSAGE_LENGTH   How can I resolve this issue I somehow guess that it is related with GCC but cannot figure out how to fix the problem. Furthermore, I have tried a PPA as suggested on  and there is a similar question for an older version of Ubuntu at . However, after I ran sudo update I get numerous warnings and the list I obtained with the strings command did not have new entries after installing gcc 4.9, so I purged the PPA() with ppa-purge. Any help, suggestions on how to proceed are greatly appreciated. Beamer itemize not aligned when in blocks While making a poster, I've got two columns with blocks with itemize inside them. MWE:  \documentclass[final]{beamer} \mode&lt;presentation&gt;{}  \usepackage{times} \usepackage{amsmath,amssymb} \usepackage[english]{babel} \usepackage[latin1]{inputenc}  \begin{document} \begin{frame}[t]{}   %\leavevmode \begin{columns}[t, onlytextwidth] \begin{column}{.5\linewidth} \begin{block}{Contributions} \begin{itemize} \item First Item \item Second Item \end{itemize} \end{block} \end{column} \begin{column}{.5\linewidth} \begin{block}{Approach} \begin{itemize} \item First Item \item Second Item \end{itemize} \end{block} \end{column} \end{columns}  \end{frame} \end{document}   My local installation and ShareLaTeX would misalign the bullets(baselines added by me):   This problem seems similar to:        But this time it happens when itemize is inside the block. If one removes the blocks it works fine.  Am I missing something or does it look like a Beamer bug?  Thanks! I'm a LaTeX noob, sorry if I missed something stupid. I am an Indian student in France on a 6 month visa for an Internship. Currently I don't have my passport with me as I have applied for UK visa and am not hoping to receive it back in next 10 days. I was wondering if I can travel to Germany without my passport in hand.   The documents I can carry are a photocopy of my passport's identity page, Residence proof here, proof of Internship in France,Indian national identity card, receipt from UK embassy stating my visa application.   Please note that I do NOT have a photocopy of French visa page. Feature request: Add pronouns to usercards? One of the questions people have raised about the new rules about pronouns is how users will know what pronouns are preferred.   We've had a trolling question which got  when the user included their preferred pronouns at the bottom of the question, and I agree that particularly on Stackoverflow (rather than sites like Interpersonal Skills or Workplace), this should be considered as 'noise' since it isn't the strict Q&amp;A this site is about. (The codez should work whatever your gender).  Currently, the suggested way of displaying your pronouns is to put it in your profile's 'About Me' section. However, this is suboptimal, since it requires opening a new page.  I suggest adding a 'preferred pronouns' field in the user profile, and displaying this on a user's usercard. There's currently a 'new contributor' label, so it could be similar to that, with she/her pronouns or whatever they choose.  In comments, it could be appended to the reputation score that currently gets shown when you hover over a name:   4,305 reputation, she/her pronouns  The default would be blank. No flair updates, no hover-in-comments update. If a user fills in this field in their profile, then it will show. How can I share files over a Windows network? I have a media computer which I recently reformatted to Ubuntu 10.04. I am probably just missing something obvious but I can't figure out how to share folders and files, so that I can browse to them on my Windows computers in order to copy files to/from the computer.  How do I do this?