When we divide $n^5+5$ by $n+5$, we get a remainder $-620$, i.e., $n^5+5=K(n+5)-620$ , now how to proceed further?
What is the maximum value of $n$ if $n + 5$ divides $n^5 + 5$, $n$ being a natural number? I tried to solve by binomial theorem but it failed.
In FreeBSD and also in Linux, how can I get the numerical chmod value of a file? For example, 644 instead of -rw-r--r--? I need an automatic way for a Bash script. I know this question is asked a lot, but the solutions I saw didn't work for me.  I only have one virtual host enabled, and I'm trying to enable access to a folder that's not under the document root  ServerAdmin webmaster@localhost DocumentRoot /var/www/html  Alias /movies /home/username/Videos/Movies  &lt;Directory /home/username/Videos/Movies/&gt;     Options Indexes FollowSymLinks     AllowOverride None     Require all granted &lt;/Directory&gt;   I set /etc/apache2/envvars as follows  export APACHE_RUN_USER=www-data export APACHE_RUN_GROUP=public   I made sure that /home/username/Videos/ and its sub folders are owned by username:public, set the permissions to 777 (after 775 didn't work) and made sure that user www-data belongs to group public.  Now, when I browse to http://localhost/movies I get  [Mon Apr 21 11:28:14.971844 2014] [core:error] [pid 1385:tid 140067725104896] (13)Permission denied: [client 127.0.0.1:46603] AH00035: access to /movies/ denied (filesystem path '/home/username/Videos') because search permissions are missing on a component of the path   But when I set /etc/apache2/envvars to run Apache under username (my own username) everything works fine. The problem is permission related, but I don't see how in my case; especially when I set the permissions to 777. Any ideas?  P.S. Ubuntu version is 14.04, Apache is 2.4.7 and I didn't edit other configuration files. Interpretation of the rating of a real transformer The rating of a real transformer is 15 kVA , 2300/230-V then can we say that the primary rms is 2300 V or can we say that the secondary rms is 230 V or both.  To clarify further, suppose to solve for certain characteristics of this transformer like primary current and secondary current i use the equivalent circuit equation of the transformer referred to the primary side as:  Vp = aVs + Req*Ip + jXeq*Ip  Then what should i use for Vp or Vs in the above equation looking at the rating of the transformer.  In the above equation looking at the rating data given above is Vp= 2300 or Vs = 230 ?As mentioned earlier the transformer is mentioned to be real. What are the shell's control and redirection operators? I often see tutorials online that connect various commands with different symbols. For example:  command1 |  command2 command1 &amp;  command2 command1 || command2     command1 &amp;&amp; command2   Others seem to be connecting commands to files:  command1  &gt; file1 command1  &gt;&gt; file1   What are these things? What are they called? What do they do? Are there more of them?    . This is on Stack Overflow. On Meta I'm able to see what the tags are on the right side of the screen. In fact, I think yesterday or some point earlier today I saw tags on the right side of the screen (I can't screenshot or remember correctly).  It's right above the asked and active heading.  I know this is minor but what happened to it? It might be useful for browsing instead of having to look at the bottom of the question post.    Found an image on Google and it shows the tags on the right side of the screen: Remove empty elements from an array in Javascript iCloud Disassociation for a Mac Computer I had a Mid-2012 MacBook Pro that recently stopped booting. I narrowed this down based on troubleshooting of the boot device to likely the SATA/hard drive connector/cable no longer working for whatever reason.  I have decided to sell the system. I'd like to know if I remove the hard drive (or in this case, an after-market SSD I've installed) from the system, will there be any other data (i.e. iCloud data) stored on the system on any other chip that I can reset in any way? I plan to reset the SMC/NVRAM before I sell the system off of to someone else.  Additionally, if I remove the hard drive, is the system still associated to iCloud (specifically Find My Mac) or any other service? If so, how do I disassociate it? The system will no longer boot even if I put in my boot device.  Thanks! In plain English, how does casting spells and using creature abilities work with the stack and priority? Who would get the longest road? Imagine the following setup. There are 3 (or more) players with an equally long road. What would happen if the longest road was broken? How is it decided who obtains the longest road from there on? Creating an index of quality from multiple variables to enable rank ordering This question is also open on EL&amp;U:   Considering the amount of controversy it aroused, I believe it's past "Learners'" level.    An edit was suggested to my sentence.     There was were an orange, some grapes, two apples and a small pile of cherries on the plate.   In my native language plurality of the verb always follows plurality of the first element on the list. There were an orange,... sounds awkward to me, no matter what follows up. My simple solution was reordering:     There were some grapes, an orange, two apples and a small pile of cherries on the plate.   But that's not the first time I faced this situation and I'd like to know what the rules of grammar say about that — was my editor overzealous or am I trying to copy rules of my language that don't apply in English? A map is continuous if and only if for every set, the image of closure is contained in the closure of image As a part of self study, I am trying to prove the following statement:  Suppose $X$ and $Y$ are topological spaces and $f: X \rightarrow Y$ is a map. Then $f$ is continuous if and only if $f(\overline{A})\subseteq \overline{f(A)}$, where $\overline{A}$ denotes the closure of an arbitrary set $A$.   Assuming $f$ is continuous, the result is almost immediate. Perhaps I am missing something obvious, but I have not been able to make progress on the other direction. Could anyone give me a hint which might illuminate the problem for me? A term for when people insist on giving you help you didn't ask for? People love to tell other people what to do. It may not be control, so much as trying to help, especially when you've asked for help directly. However, there's a difference between answering someone's question and answering while piling on recommendations the person didn't ask about, and this is what I'm seeking a term for. Advertising and marketing feel similar to me in this vein. In the worst cases this can be overzealous religious followers professing your damnation if you don't follow with them (I think in Christianity they call it "witnessing"). Any which way, it comes across to me as a form of unsolicited advice: I didn't ask for it, so I don't want it; I want to stay focused.  Is there a better term for this than "unsolicited advice"? Also, is there a term for a person who exhibits this kind of behavior frequently? So, I was just assaulted by a trio of fairly well armed thugs while walking out of Riften. Before attacking me, they informed me that they were 'here to teach me a lesson.'  After dispatching them in due course, I found this on the body of what I can only assume to be the leader, given his vastly superior armaments:   Orgnar is the innkeeper in Riverwood. Now, I admit, I've stolen a fair amount, but I pride myself on having never been caught. My total bounty to date is at zero. So, how did he figure out that I stole something, why is he taking the law into his own hands, and if I go back to Riverwood, am I going to get shanked? Which is the right way to do something like 'description' list but with customizable and fixed-width labels? I.e. something like this:  Label:         Text text text text text text                text text text text. Longer label:  Text text text text text text                Text text text text.   The way I see it to use two-column table (first columt for labels and second column for descriptions), but this solution seems ugly. Is there any other way? How do I run 32-bit programs on a 64-bit Debian/Ubuntu? I have a 64-bit (amd64 a.k.a. x86_64) Debian or Ubuntu installation. I need to run 32-bit (i386/i686) programs occasionally, or to compile programs for a 32-bit system. How can I do this with a minimum of fuss?  Bonus: what if I want to run or test with an older or newer release of the distribution? Crick’s Central Dogma — Counter Cases Are Love Potions legal? linear dependence proof using subsets Why doesn't Steam start? When I try to start Steam nothing happens. Reinstall doesn't help.  $ steam Running Steam on ubuntu 13.04 64-bit STEAM_RUNTIME is enabled automatically Installing breakpad exception handler for appid(steam)/version(1378500910_client) Installing breakpad exception handler for appid(steam)/version(1378500910_client) Installing breakpad exception handler for appid(steam)/version(1378500910_client) unlinked 0 orphaned pipes removing stale semaphore last operated on by process 7278 with name 0eBlobRegistryMutex_DC7EBB4AEA41D3C6C74E5EFFD6757CEC removing stale semaphore last operated on by process 7278 with name 0eBlobRegistrySignal_DC7EBB4AEA41D3C6C74E5EFFD6757CEC removing stale semaphore last operated on by process 7278 with name 0emSteamEngineInstance removing stale semaphore last operated on by process 7278 with name 0eSteamEngineLock Gtk-Message: Failed to load module "overlay-scrollbar" Installing breakpad exception handler for appid(steam)/version(1378500910_client) [0913/182910:WARNING:proxy_service.cc(958)] PAC support disabled because there is no system implementation   How to fix it?