A student of mine has asked me to solve the following Diophantine equation, but it has been a long time since I looked at these problems. Here is the problem:  Problem: Find the natural number solutions of the equation $$a+b+c+d+e = 2020.$$  Any help is appreciated.
How to use the  method?  Say I want to find number of combinations I can get with $x_1+x_2+x_3+x_4=22$,  where $x_i\in\mathbb{N}$.  Is this the correct time to apply the method?  This is being repurposed in an effort to cut down on duplicates, see here:     and here:
Where does tidal energy come from? Undo apt-get remove open* ubuntu 12.04 After two days of installation, strangely my Ubuntu machine is restarting instead of shutdown from both desktop GUI and command line.  sudo shutdown -h now sudo halt  # (doesn't shutdown, instead freezes on boot screen Plymouth)   I had force shutdown by powering off the machine.  This is not happening all the times.  I have been using Ubuntu for 6 months and never experienced this kind of problem. We were discussing Kirchoff's theorem on blackbody radiation in class today and the equation was: $$e_{f}= J(f,T)$$  $e_f$ was defined as power per unit area per unit frequency. What does per unit frequency refer to here? I know what per unit time means but don't understand 'per unit frequency'. Recommendation for mobile prepaid SIM card for smartphone + home calls in Germany What SIM card would you recommend for a smartphone user for travel in Germany?  It would be probably the only or the most important connection to the Internet, so large amounts of data and relatively fast transfer is an issue.  I need to stay in touch with friends and family, so the calls to other EU countries should be as cheap as possible.   For to the first criteria, I found the T-Mobile offer interesting. The internet costs 10 Euros/month and after reaching the transfer limit it stays relatively fast. According to tests (Galileo from Pro7, AFAIR) it has also the best coverage. However, calls to other countries are very expensive.  For to second criteria, Lebara and Mobilka are interesting. The calls are very cheap, but there are problems with signal strength in many locations, where T-Mobile has no problem. The voice quality, at least in Lebara, is also limited. They both have mobile internet with unlimited transfer, but after reaching the high speed limit, the transfer is reduced to 64 kbps, which is too slow.  I've found out that O2 has foreign calls at moderate prices, but I haven't yet checked for details. There are so many other options, making it is hard to compare them all without spending the whole weekend on it. So, if someone has found a better option than having 2 SIM cards and constantly switching them, this answer would be greatly appreciated. Making a div vertically scrollable using CSS Why do we have two of some organs, but not all? We have two eyes, but we don't have two hearts. Why do humans have two of some organs, but not all? How to use Boost in Visual Studio 2010 boolean[] vs. BitSet: Which is more efficient? What is more efficient in terms of memory and CPU usage — an array of booleans or a BitSet? Specific BitSet methods are not used, only get/set/clear (==, =, Arrays.fill respectively for an array). Is it possible to do The Pitt without a slave outfit? On the three Stack Overflow chat servers, the  page displays the following image:    Is it from an actual episode, or is it a 'shop? Is 1+1 =2 a theorem? A theorem is defined to be a mathematical statement that is proven to be true. The statement $1+1=2$ has definitely been proven in the history of mankind (Russel and Whitehead had once proven it in the book Principia Mathematica).   So can it be considered as a theorem? What determines something to be a theorem (besides it being proven to be true)? How can a capacitive touch screen be triggered without human contact? I want to robotically touch an iPhone screen without any human intervention.   I've done some experiments but have not found a reliable solution. It seems even styluses that work through gloves still rely on the capacitive characteristics of the human body.    Carrot held by human works Carrot held in plastic clamp doesn't Pogo Stylus works held by human and held by human through clothes Stylus does not work held in plastic clamp.  Stylus works held in plastic clamp attached to human through clothes via jump lead. Stylus held in plastic clamp with jump lead dangling off seems to work most the time.   Is it possible to mimic the human element using capacitors and other components? What signal does the capacitive screen need to be triggered?  Thanks Did Luke attempt to retake the Jedi Temple on Coruscant? After the New Republic gains control of Coruscant through the Galactic Concordance, did Luke Skywalker attempt to reclaim (or even visit) the former and still very much intact Jedi Temple, now converted to be the deceased Emperor's palace?   If Luke is so insistent on saving a tree just because it belongs to the Jedi and the Empire stole it, then shouldn't reclaiming the Jedi Temple be even higher priority?  If he did, is he aware of the Sith shrine beneath it? Which is something even Yoda does not know. And if he didn't, why didn't he? What are the good ways to migrate a RAID array to bigger disks? I understand that there is an upper limit. But why do you have to type at least 15 characters to post a comment? It is easy to work around it anyway (like adding dots or other useless things). Is there a shortcut for switching between these three modes? I wrote a bash script as below:  #!/bin/bash echo "Enter a file name" read filename import -window root $HOME/Desktop/$filename.png   I expected this script to take a screen shot and save the image with the given filename on my desktop.  Problem:  My Ubuntu terminal is giving error:     import: Command Not Found Can I use 'in' instead of 'at'? -- "I have more books in my house." I am learning English using the Duolingo English course, one of correct solution was      I have more books at my house.   Can I use      I have more books in my house.   If it is OK, what is the difference between both? Electorate badge rules? I just got the  badge on StackOverflow, which is nice, but I noticed a number of top users aren't yet listed (inluding Jon Skeet and Marc Gravell, who would certainly qualify).  This made me wonder how the badges are retrospectively applied. Is it just that the display is heavily cached and the badge is awarded when the user logs in again or something?