What is the remainder when $2^{2016}$ is divided by $47$?   I have done Fermat's little theorem and I have now this:  $2^{2016} \equiv 2^{38} \pmod{47}$  My issue is that $2^{38}$ is too large of a number to work with, how do I continue?
How do I efficiently compute $a^b\bmod c$:  When $b$ is huge, for instance $5^{844325}\bmod 21$? When $b$ is less than $c$ but it would still be a lot of work to multiply $a$ by itself $b$ times, for instance $5^{69}\bmod 101$? When $(a,c)\ne1$, for instance $6^{103}\bmod 14$?  Are there any other tricks for evaluating exponents in modular arithmetic?  This is being asked in an effort to cut down on duplicates, see  and .
In Java Edition, I can name a mob by using NBT tags like this: /summon zombie ~ ~ ~ {CustomName:'{&quot;text&quot;:&quot;TheUndead&quot;}'}  But in Bedrock Edition, I've heard NBT is not accessible from commands. What can I do to summon a mob with a custom name tag using the /summon command? How to compute the topological space of fibered product of schemes? $(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$ Let $\sim$ be the equivalence relation on $S_1 \times I$ given by $(x,t)\sim(y,s)$ if and only if $xt=ys$ where $I=[0,1]$  How do I prove that $(S_1 \times I)/\sim$ is homeomorphic to the unit disk $D^2$ with the induced topology? how does the circuit of a basic Variable speed electric drill work? i am trying to 'automate' the control of an electric drill motor that im taking from a garden variety Variable Speed drill (from Harbor Freight)  it has a universal AC motor which I basically undertand and a DPDT switch to reverse direction and a triac citcuit to vary speed    Question 1 . i see 4 wires going to the 'field/Stator coil(s)'. Are there 2 seperate field/stator coils here? is this to provide low/high power.  I think in theory , you only need 1 coil with 2 wires and that coil is wired in series with the brushes... is that right?   how does this circuit work with 2 coils.  Question 2 . how does this variable speed circuit work.  is the wiring diagram correct (it doesnt show a variable resistor and it doesnt show what drives the control input of the traic? why are there two switches in the thing? does switch 2 close at high speed and thus shunt around the triac?  please see the attached 4 diagrams How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$ How to solve the following functional equation:  Find all $f:\mathbb{R}\to\mathbb{R} $ such that: $$ f\left(x^2+f(y)\right)=y+f(x)^2 $$ Holds for every $x,y\in\mathbb{R}$.  A friend gave it to me, probably its an olympiad question.  I started with the equation $f(f(y))=y+f(0)^2$ which seems to be quite helpful, but I couldn't do it effectively. How to solve it properly? jQuery scrolltop firefox not working Does Time Machine backup programs like Photoshop and iWork? How long is a 'block'? Is there a Google Drive client available? I have to travel to Germany and Switzerland for business purpose. I have already been here 2 years ago. I have applied for business visa to the German consulate twice and both times the application got rejected. They have put a green stamp on the last page twice. The reason is the purpose and information submitted regarding intended stay is not reliable. I have submitted the documents to Swiss consulate and they have accepted and granted me a visa. Now I have to first travel to Germany and then to Switzerland.  So my question is, with a Schengen business visa granted by Switzerland, may I enter in Germany? Does the rejection stamp has any impact for entering at German airport ? Does it mean I cannot travel to Germany but to other Schengen countries ? Can quarks be considered real and elementary? "happen to be" and "happen to have" - expressions of probability? Based on Logman dictionary:       happen to do something: if you happen to do something, you do it by chance.   for example take a look at these examples:     They happen to be unemployed at the time. I happen to have a degree in computer science.    So based on the definition of the happen to do something, first one means they are probably unemployed at the time. and the second one means I probably have a degree in computer science.     Am I right? I'd like to find an analogue of  or any other fps counter on Ubuntu 12.10.  After some googling I found 2 solutions:   To use  (I found it from ). This solution didn't work for me because after launching the game:  mumble-overlay game   I got this error:  game: symbol lookup error: /usr/lib/mumble/libmumble.so.1: undefined symbol: glPopClientAttrib   And I didn't find any fix of this error in the WEB. To use WINEDEBUG=fps with osd_cat. It works only with  (only Windows games). Found from reading  and . It shows FPS during play but the output is definitely wrong - 0.15-0.18 fps. And it doesn't matter if game really runs slow or fast - the result is always the same.   Does anyone know how to fix these errors? Or are there any other solutions? Thanks for the help. Surface of genus $g$ does not retract to circle (Hatcher exercise) I am from Bangladesh, and I have an Indian tourist visa, which I received from the Indian High Commission in Bangladesh. At this moment I am in Bhutan. Now I want to enter India by air. Is it possible? And will I face any problems when I come back from Kolkata to Dhaka? I have often heard people say "x of his" or "x of mine". But since his and mine point out ownership, isn't using "of" here doubles that ownership? Wouldn't it be more appropriate to say "x of him" or "x of them" etc.?  Example:     I was a good friend of your dad's. He told me all about you` I currently have a Yongnuo YN560-TX trigger and a Yongnuo YN-560 Mark III. I would like to get a iTTL flash that also works with remote triggering.  How compatible are are different flash brands (Neewer, Yongnuo, etc.) when it comes to things like setting zoom, etc. ? I'm trying to figure out how to assign higher priority to one PPA over another PPA. I had a look on bunch of the answers on this forum but none of them solves my problem.  We have two PPA sources on some of our servers which we stick into separate files in /etc/apt/sources.list.d . Some of these repos provide same packages (in terms of names) but different versions and possibly different binaries. Is there a way how we can PRIORITISE one repo over another ?  I read apt_preferences tutorial but it could not be more obscure and didn't find the answers for my question. Here is the situation. WE have the following sources:  $ ls -l /etc/apt/sources.list.d  total 12 -rw-r--r-- 1 root root 66 Jan  2 16:50 nginx-source.list -rw-r--r-- 1 root root 84 Jan  2 16:49 ruby-ng-experimental-source.list   where nginx-source.list content is:  deb     http://ppa.launchpad.net/nginx/stable/ubuntu precise main   and ruby-ng-experimental-source.list content is:  deb     http://ppa.launchpad.net/brightbox/ruby-ng-experimental/ubuntu precise main   Both of these sources provide nginx-full package of different versions etc. When I list the priorities ruby-ng-experimental-source.list is on top of output hence nginx-full is installed from that repo:  $ apt-cache policy nginx-full                                  nginx-full:   Installed: 1:1.2.3-1~38~precise1   Candidate: 1:1.2.6-1~43~precise1   Version table:      1:1.2.6-1~43~precise1 0         500 http://ppa.launchpad.net/brightbox/ruby-ng-experimental/ubuntu/ precise/main amd64 Packages  *** 1:1.2.3-1~38~precise1 0         100 /var/lib/dpkg/status      1.4.1-1ppa0~precise 0         500 http://ppa.launchpad.net/nginx/stable/ubuntu/ precise/main amd64 Packages      1.1.19-1ubuntu0.1 0         500 http://mirror.rackspace.co.uk/ubuntu/ precise-updates/universe amd64 Packages      1.1.19-1 0         500 http://mirror.rackspace.co.uk/ubuntu/ precise/universe amd64 Packages   How do I prioritize repo listed in nginx-source.list over the one which is on top of the list now ? I tried something like this:  $ cat /etc/apt/preferences Package: nginx-full Pin: origin http://ppa.launchpad.net/nginx/stable/ubuntu Pin-Priority: 1000  Package: nginx-full Pin: origin http://ppa.launchpad.net/brightbox/ruby-ng-experimental/ubuntu Pin-Priority: 100   But that has changed priorities of both sources to the same number - or something like that ? So this has NOT changed the priorities and nginx-full is still being installed form the brightbox PPA  $ apt-cache policy nginx-full   nginx-full:   Installed: 1:1.2.3-1~38~precise1   Candidate: 1:1.2.6-1~43~precise1   Package pin: (not found)   Version table:      1:1.2.6-1~43~precise1 1000         500 http://ppa.launchpad.net/brightbox/ruby-ng-experimental/ubuntu/ precise/main amd64 Packages  *** 1:1.2.3-1~38~precise1 1000         100 /var/lib/dpkg/status      1.4.1-1ppa0~precise 1000         500 http://ppa.launchpad.net/nginx/stable/ubuntu/ precise/main amd64 Packages      1.1.19-1ubuntu0.1 1000         500 http://mirror.rackspace.co.uk/ubuntu/ precise-updates/universe amd64 Packages      1.1.19-1 1000         500 http://mirror.rackspace.co.uk/ubuntu/ precise/universe amd64 Packages   Anyone has any idea how to achieve what I'm trying to do ? was closed as "Not constructive" a little while ago by CasperOne. I'm not here to argue about the closure; in fact, I'm forced to agree that, as it stands, the question is explicitly a polling question and eligible to be closed for that reason.  I'd like to see it preserved, however; it's got a fair bit of useful in-depth information for ObjC/Cocoa developers on the "singleton" topic.* It's also (possibly more importantly) a great duplicate target -- have a look at the list of linked questions. I want to try to stave off deletion, and hopefully get it reopened.** (I did vote for reopening, but it expired.)  My thought is to edit the question itself into a "constructive" form, but after spending some time pondering how to do so, I'm not crazy about any of the ideas that I've come up with. Essentially they all involve reworking the question to fit the answers:   Rewrite the question so that the accepted answer fits exactly. "I've got this singleton implementation, but I really want the creation to happen earlier in my app's execution. How can I make that happen?" This is artificial and (in my opinion) doesn't make a particularly good question. Make the question still general, but more concrete and focused on the implementation give in the body. "What are the pitfalls associated with this singleton creation procedure? Are there other features that my singleton should have?" This is still skirting the border of discussion->NC, and none of the answers really respond to this exactly. Remove the implementation from the question and just ask for the "best" implementation. This obviously requires coming up with stringent criteria for "best", and, while it would preserve the relationship between the Q and A's best, might not even move it out of NC territory.   I'm looking for suggestions of ways to re-write this so that it can stick around. Alternatively, if you think I should just be advocating for a historical lock, say so.   If you think my basic premise is faulty and don't think the question should be preserved at all, I respectfully request that you just downvote me instead of answering -- I'd prefer not to turn this into an argument about the merits of the question, and I definitely don't want it to become a(nother) "deletionist"/"inclusionist" skirmish (and I am not infrequently ).    *Quite a bit of it unfortunately in comments.  **Historical locking would also be an acceptable solution to me, but it doesn't seem to fit the "controversial" criterion. How to change Blender's default startup settings? How can I change Blender from the default cube/lamp/camera default setup? Also, is it possible to change other features, such as the default view direction (Top, Side, etc) or the Editor type (3D View, Node Editor, Graph Editor, etc)?