I am trying to find the given sum modulo prime  Given n integers and a number $D$ you have to calculate $(a_1 + a_2 + \cdots + a_n)^D$  but the twist here is that there coefficient should not be considered in sum ;  e.g  $(a+b)^2 = a^2 + b^2 + 2ab$;  But , required sum is $a^2 + b^2 + ab$;  e.g  $(2+6+7)^2=15^2=225$  But , required sum is : $2^2 + 6^2 + 7^2 + 6\cdot7 + 2\cdot7 + 2\cdot6 = 157$  Constraints :   $N\le5000$ (elements where each element $\le10^5$)  $D\le10^{18}$; (Power)  Any hint will be helpful :)
I'm looking for a formula to calculate the sum of $(a+b+c+d+...)^n$ but with coefficients equal to 1. For example in $(a+b+c)^2$. I want the sum of $a^2 + b^2 + c^2 + ab + bc + ca$. And for $(a+b+c+d)^3$, I want the sum of $a^3 + b^3 + c^3 + a^2b + a^2c + b^2a + b^2c + c^2a + c^2b + abc$. Similarly, I want the sum of expansion of $(a+b+c+d+e+....)^n$ with coefficient equal to 1. I tried to find the pattern by expanding the $(a+b+c)^2$. And I found that its formula is $a^2 + b^2 + c^2$ + $\frac{((a+b+c)^2 - a^2-b^2-c^2)}{2}$. This works for the power of 2. But fails on other powers. Any help will be really appreciated.
What's with those who ask a question, but don't ever seem to come back to add requested info? On stackoverflow, there seem to be quite a few programmers who ask a question, usually with one line like:  "How do I release memory after memory warning? My app crashes. Thanks and welcome for reply."   And a bunch of us will ask questions like   what platform? give us some more detail about the crash.   Weeks will go by and the original poster never adds any more details.  In the meantime, some respondents go ahead and answer the question thoroughly, covering possible platforms/scenarios, etc.  Of course no answer is ever selected by the OP.  Then the OP shows up again, and asks another question, sometimes its the same question asked differently, sometimes not.    What is going on here?  Do they have one chance every so often to get a query out on the Internet and they get through and they post and then they can't get back?  Or are they forgetful, since they are posting the same question to tens or hundreds of sites?    I'm just curious.  Seems like they shoot themselves in the foot when they have a captive audience waiting for more details of their problem, yet they never provide those details. Why is polynomial regression considered a special case of multiple linear regression? If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression?  Wikipedia notes that "Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function $\mathbb{E}(y | x)$ is linear in the unknown parameters that are estimated from the data."  How is polynomial regression linear in the unknown parameters if the parameters are coefficients for terms with order $\ge$ 2? What is the double slash (//) directory? I mistakenly typed cd // instead of cd /. To my surprise, current directory showed up as //.   What is that directory? Why does it exist?  apple@snipped $ pwd /home/apple apple@snipped $ cd / apple@snipped $ pwd / apple@snipped $ cd // apple@snipped $ pwd // apple@snipped $ cd /// apple@snipped $ pwd / Freeze vertical columns in horizonal scrolling visual force page (like excel freeze pane) let's say have 20 columns total.   I want to fix till 5 columns. (means only important ID, etc will be fixed while doing horizonal scrolling)  How can I achieve it in Visual Force Datatable ? In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.   I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it.        I strongly believe in the following quote:     You do not really understand something unless you can explain it to your grandmother. -- Albert Einstein   Well, I can't explain these concepts to a layman or grandma.   Why PCA, eigenvectors &amp; eigenvalues? What was the need for these concepts? How would you explain these to a layman? VMware Linux Server -- how can you tell if you are a vm or real hardware? Interface naming in Java Most OO languages prefix their interface names with a capital I, why does Java not do this?  What was the rationale for not following this convention?  To demonstrate what I mean, if I wanted to have a User interface and a User implementation I'd have two choices in Java:        Class = User, Interface = UserInterface   Class = UserImpl, Interface = User      Where in most languages:     Class = User, Interface = IUser   Now, you might argue that you could always pick a most descriptive name for the user implementation and the problem goes away, but Java's pushing a POJO approach to things and   most IOC containers use DynamicProxies extensively.  These two things together mean that you'll have lots of interfaces with a single POJO implementation.  So, I guess my question boils down to: "Is it worth following the broader Interface naming convention especially in light of where Java Frameworks seem to be heading?" Beamer: \nonumber equivalent for slides? Is there an equivalent command to \nonumber when one doesn't want to include certain slides in the numbering? I would like to leave outline and title slides out of my numbering, and instead just number slides with actual content. Other workarounds would be nice to know about as well.  Edit: Since a MWE example was requested, here is one. Suppose I have a title page and two other slides. The code below gives a slide counter that goes up to 3, and the title slide is slide 1. I would prefer to have the title slide not be numbered, the counter go up to 2, and the the numbering start at the slide after the title. Here is some code.  \documentclass{beamer}  \mode&lt;presentation&gt;  {    \usetheme{Dresden}  }   \setbeamertemplate  {footline}{\quad\hfill\insertframenumber/\inserttotalframenumber\strut\quad}    \begin{document}  \begin{frame}  \titlepage \end{frame}  \begin{frame} Some actual content here \end{frame}  \begin{frame} Some more actual content here \end{frame}  \end{document} What do the bars between keyframes mean? What inspired Tauriel's story arc? I know Tauriel is a Jackson created character, but I wondered if anywhere in the legendarium there was fodder for the story arc between her and Kili.  I do not have access to all my books for the time being and recall stories of love between men and elves in the Silmarillion and Appendices but don't remember any such stories between elves and dwarves and wondered if there was any basis of inspiration for this aspect of their relationship within Tolkien's works.   This movie, of course, departs even further from the original than those made before it, but as a story unto itself, I can still appreciate the ride, so if there is no Tolkien basis, what inspired Jackson, Boyens, and Walsh to create this particular arc?  Is there interview info or anything? Should academic papers necessarily carry a sober tone? I was reading  titled "Optimal Symmetric Rendezvous Search on Three Locations." While talking about the history of search problems, the author mentions the following anecdote in passing.     In 2007 a letter writer to the Guardian newspaper queried, “I lost my wife in the crowd at Glastonbury (a music festival). What is the best strategy for finding her?” A reader replied, “Start talking to an attractive woman. Your wife   will reappear almost immediately.”   While I found it quite amusing to read this, I do not often come across papers with such witticisms. Is there an unwritten rule about the tone of sobriety that is considered appropriate in academic papers? Are jokes or anecdotes fine as long as they do not appear forced? I'm creating a model for a 3D game that will eventually be exported using a custom Python script. This model makes heavy use of UV textures.  However, the project now references a bunch of images that are not used by any objects in the project. Example:    I don't want the first two, or the red_bubble.png image. However, I have no idea how to remove them from the project. Selecting one of them reveals that there are "2 users of the data" although I am not using it anywhere.  How can I get rid of these excess images? How to use \graphicspath? I am using MikTex 2.9 and TeXstudio for my TeX preparation. I would like to set the path to my figures folder, which contains all the figures, plots etc. required for my work.   I used \graphicspath to set the directory, but it gives me an error message:  \documentclass[12pt]{article}  \usepackage{graphicx}  \graphicspath{D:/LATEX/Reports@IIT/figures}  \begin{document} \includegraphics[width=4.5cm,height=4cm,angle=0]{logo.jpg}  \end{document}      Error: Package pdftex.def Error: File `logo.jpg' not found   However, when I prepend the filenames of the images with the same path in the \includegraphics command, it works just fine:  \documentclass[12pt]{article}  \usepackage{graphicx}  \begin{document}  \includegraphics[width=4.5cm,height=4cm,angle=0]{D:/LATEX/Reports@IIT/figures/logo.jpg}  \end{document}   Why is \graphicspath not setting the path? What is the scope of variables in JavaScript? How to hide the [@] in a Minecraft command block How do I get horizontal lines to the left and right of a heading in Microsoft word? In Word 2007 I want to put a heading in the center of a line with a horizontal line to the left and to the right of the text.  The line must not cross through the text. I have tried using autoshapes and lines - but then the lines move each time I press Enter or &larr; Backspace and I have to put them in place again manually.  At Borders and Shading there is an "Insert horizontal line" option, but this gives me a solid line from the left to the right of the page and I cannot insert text anywhere on it or in it.    The final product should look something like this:     -------------------------  Heading ------------------------- Why cant I navigate to lightning component in communities? Im on a lightning community, i have a lightning component and i want to open another component with this code:  navigateToMyComponent : function(component, event, helper) {     console.log('1');     var evt = $A.get("e.force:navigateToComponent");     console.log('2');     evt.setParams({         componentDef : "c:CompetenciaComponent"     });     console.log('3');     evt.fire();     console.log('4'); }   this its the console log:   NOTHINGS HAPPEND AND I DONT KNOW WHY What is the difference between "var=${var:-word}" and "var=${var:=word}"? A hidden process, what it is? [root@datacenteronline ~]# ssh root@192.168.1.172 Last login: Wed Apr 17 09:55:45 2013 from 192.168.1.187 [root@localhost ~]# ls /proc/ | grep 2266 [root@localhost ~]# cd /proc/2266 [root@localhost 2266]# ls attr             cpuset   limits      net            root       statm autogroup        cwd      loginuid    numa_maps      sched      status auxv             environ  maps        oom_adj        schedstat  syscall cgroup           exe      mem         oom_score      sessionid  task clear_refs       fd       mountinfo   oom_score_adj  smaps      wchan cmdline          fdinfo   mounts      pagemap        stack coredump_filter  io       mountstats  personality    stat [root@localhost 2266]# ls -al /proc/2266 total 0 dr-xr-xr-x   7 apache apache 0 Apr 17 09:45 . dr-xr-xr-x 266 root   root   0 Apr 17 09:11 .. dr-xr-xr-x   2 apache apache 0 Apr 17 09:45 attr -rw-r--r--   1 root   root   0 Apr 17 09:45 autogroup -r--------   1 root   root   0 Apr 17 09:45 auxv -r--r--r--   1 root   root   0 Apr 17 09:45 cgroup --w-------   1 root   root   0 Apr 17 09:45 clear_refs -r--r--r--   1 root   root   0 Apr 17 09:45 cmdline -rw-r--r--   1 root   root   0 Apr 17 09:45 coredump_filter -r--r--r--   1 root   root   0 Apr 17 09:45 cpuset lrwxrwxrwx   1 root   root   0 Apr 17 09:45 cwd -&gt; / -r--------   1 root   root   0 Apr 17 09:45 environ lrwxrwxrwx   1 root   root   0 Apr 17 09:45 exe -&gt; /usr/local/apache2/bin/httpd dr-x------   2 root   root   0 Apr 17 09:45 fd dr-x------   2 root   root   0 Apr 17 09:45 fdinfo -r--------   1 root   root   0 Apr 17 09:45 io -rw-------   1 root   root   0 Apr 17 09:45 limits -rw-r--r--   1 root   root   0 Apr 17 09:45 loginuid -r--r--r--   1 root   root   0 Apr 17 09:45 maps -rw-------   1 root   root   0 Apr 17 09:45 mem -r--r--r--   1 root   root   0 Apr 17 09:45 mountinfo -r--r--r--   1 root   root   0 Apr 17 09:45 mounts -r--------   1 root   root   0 Apr 17 09:45 mountstats dr-xr-xr-x   6 apache apache 0 Apr 17 09:45 net -r--r--r--   1 root   root   0 Apr 17 09:45 numa_maps -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_adj -r--r--r--   1 root   root   0 Apr 17 09:45 oom_score -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_score_adj -r--r--r--   1 root   root   0 Apr 17 09:45 pagemap -r--r--r--   1 root   root   0 Apr 17 09:45 personality lrwxrwxrwx   1 root   root   0 Apr 17 09:45 root -&gt; / -rw-r--r--   1 root   root   0 Apr 17 09:45 sched -r--r--r--   1 root   root   0 Apr 17 09:45 schedstat -r--r--r--   1 root   root   0 Apr 17 09:45 sessionid -r--r--r--   1 root   root   0 Apr 17 09:45 smaps -r--r--r--   1 root   root   0 Apr 17 09:45 stack -r--r--r--   1 root   root   0 Apr 17 09:45 stat -r--r--r--   1 root   root   0 Apr 17 09:45 statm -r--r--r--   1 root   root   0 Apr 17 09:45 status -r--r--r--   1 root   root   0 Apr 17 09:45 syscall dr-xr-xr-x  29 apache apache 0 Apr 17 09:45 task -r--r--r--   1 root   root   0 Apr 17 09:45 wchan   Cound anyone tell me what it is? Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems?