How many pairs of integers satisfy a cubic diophantine equation?
Solve the equation $x^3 + 117y^3 = 5$ over the integers.
Problem with sudo apt update in Ubuntu 18.04: Post-Invoke-Success if /usr/bin/test -w /var/lib/command-not-found/ The terminal gave me these errors when updating the software with sudo apt update.    Hit:1 http://it.archive.ubuntu.com/ubuntu bionic InRelease Hit:2 http://it.archive.ubuntu.com/ubuntu bionic-updates InRelease                                                                                        Hit:3 http://it.archive.ubuntu.com/ubuntu bionic-backports InRelease                                                                                      Hit:4 http://security.ubuntu.com/ubuntu bionic-security InRelease                                      Hit:5 http://archive.canonical.com/ubuntu bionic InRelease                 Traceback (most recent call last):                       File "/usr/lib/cnf-update-db", line 8, in &lt;module&gt;     from CommandNotFound.db.creator import DbCreator ModuleNotFoundError: No module named 'CommandNotFound' Reading packages list... Done E: Problem executing scripts APT::Update::Post-Invoke-Success     'if /usr/bin/test -w /var/lib/command-not-found/ -a -e /usr/lib/cnf-update-db;       then /usr/lib/cnf-update-db &gt; /dev/null; fi'   E: Sub-process returned an error code     These are the results of sudo apt install --reinstall command-not-found  Reading package lists... Done  Building dependency tree         Reading state information... Done 0 upgraded, 0 newly installed, 1 reinstalled, 0 to remove and 0 not upgraded. Need to get 0 B/5.188 B of archives After this operation, 0 B of additional disk space will be used. (Reading the database ... 225797 files and directories currently installed.) Preparations for extracting ... / command-not-found_18.04.4_all.deb ... Extracting command-not-found (18.04.4) on (18.04.4) ... Configuring command-not-found (18.04.4) ... libdvd-pkg: Package libdvdcss2-1.4.2-1 was removed, stop processing...   When I tried the command sudo apt update again after reinstalling command-not-found, the results were the same as described in the first text block. How to find manually installed packages? I installed a plain Ubuntu 10.10 on my computer and installed some software via apt-get. Last week I managed to break everything and just started from scratch, and I need to reinstall my software. Is there some way to create a list with all the packages that I have installed manually?  So that it would give me a list like texlive, ... and not texlive, texlive-dep1, textlive-dep2, ... and all the standard packages removed?  If I could somehow figure out which programs out of the regular install I have removed, that would be awesome too!    Update 2015-05-23: I now use Ansible as configuration management on my systems. There I specify the packages to install. This serves the goal, installing all the programs on a fresh system, even better. So this question might be the entry into some light configuration management. Keras - no prediction probability for multiple output models? Get three highest values from the array I am developing my first 2D game in Unity and I have come across what seems an important question.  How do I handle data between scenes?  There seems to be different answers to this:   Someone mention using , while other people told me this should be used to store other things like screen brightness and so on. Someone told me that the best way was to make sure to write everything into a savegame everytime that I changed scenes, and to make sure that when the new scene loads, get the info from the savegame again. This seemed to me wasteful in performance. Was I wrong? The other solution, which is the one I have implemented so far is to have a global game object that isn't destroyed between scenes, handling all the data between scenes. So when the game starts, I load a Start Scene where this object is loaded. After this ends, it loads the first real game scene, usually a main menu.   This is my implementation:  using UnityEngine; using UnityEngine.UI; using System.Collections;  public class GameController : MonoBehaviour {      // Make global     public static GameController Instance {         get;         set;     }      void Awake () {         DontDestroyOnLoad (transform.gameObject);         Instance = this;     }      void Start() {         //Load first game scene (probably main menu)         Application.LoadLevel(2);     }      // Data persisted between scenes     public int exp = 0;     public int armor = 0;     public int weapon = 0;     //... }   This object can be handled on my other classes like this:  private GameController gameController = GameController.Instance;   While this has worked so far, it presents me with one big problem: If I want to load directly a scene, let's say for instance the final level of the game, I can't load it directly, since that scene does not contain this global game object.  Am I handling this problem the wrong way? Are there better practices for this kind of challenge? I would love to hear your opinions, thoughts and suggestions on this issue.  Thanks How do I cd into a directory in the home folder? How do I change directories to downloads, from the home folder, in the latest version Ubuntu 12.10? I tried cd /downloads, but it gave an error saying that there is no such directory. I just did my first install of any Linux OS, and I accidentally selected "Desktop GUI" in the install, but I want to build everything myself. Is there any way by which I can remove the GUI environment without re-installing OS? Prove that if $g^2=e$ for all $g$ in $G$ then $G$ is Abelian. Find all solutions to $x^9 \equiv 25 \pmod {29}$ What is PECS (Producer Extends Consumer Super)? Let $U$ be connected. A function $u \in H^1(U)$ is a weak solution   of Neumann's problem   \begin{equation} (*)\qquad\left\{ \begin{array}{rl} -\Delta = f &amp; \text{in } U \\ \frac{\partial u}{\partial \nu} = 0 &amp; \text{on } \partial U \end{array} \right. \end{equation}   if   $$ \int_U Du \cdot Dv \; dx = \int_Ufv \; dx $$   for all $v \in H^1(U)$. Let $f\in L^2(U)$. Prove $(*)$ has a weak solution   if and only if   $$ \int_U f \; dx =0. $$   For the only if part I set $v=1$. However I do not see where to start the if part. I was thinking of the Lax-Milgram theorem. That's where I'm now. How can I copy the contents of a folder to another folder in a different directory using terminal? I am trying to copy the contents of a folder to another folder in a different directory using terminal.  Would somebody be able to provide me an example of the command line syntax required to achieve this? When I dip a paper towel in a cup of water the water gets drawn up due to . How is this reconciled with conservation of energy, as it would seem on the surface that the potential energy of the system has gone up with no work being done? Title says it all I looked for a proof on this site but couldn't find one.  Prove if $f$ is analytic on $D$ and $g$ is analytic on $\Omega$ containing the range of $f$ show $g(f(z))$ is analytic.  The statement seems obvious but I can't seem to be able to prove it. The tilde operator in Python Firefox 33 doesn't see Java Plugin I am trying to enable Java (not JavaScript) in my Firefox v. 33 so that I can use applets within the browser.  Currently, I just get a dark gray box across the whole screen when I try to load an applet, without any error message or prompt to install plugin.  As per , I tried going into the Firefox plugin page to activate it, however, it wasn't there listed.  I do have Java 7 installed and it is in the path:  &gt;java -version java version "1.7.0_71" Java(TM) SE Runtime Environment (build 1.7.0_71-b14) Java HotSpot(TM) 64-Bit Server VM (build 24.71-b01, mixed mode)   What do I need to do to get Firefox to see my Java installation and recognize it as a plugin so that I can enable it and view applets inside the browser? Convergence of Ratio Test implies Convergence of the Root Test I always wondered on what algorihm the best league of mine is chosen.    I am in the 0.16% of this quarter. That is rank 171 this quarter. But I am also ranked 113th this month.  Why is the stat for the quarter displayed when I have a better ranking in the month? I would like to capture the contents of AJAX requests using Greasemonkey.  Does anybody know how to do this? Is it always better to use the whole dataset to train the final model? A common technique after training, validating and testing the Machine Learning model of preference is to use the complete dataset, including the testing subset, to train a final model to deploy it on, e.g. a product.      My question is: Is it always for the best to do so? What if the   performance actually deteriorates?   For example, let us assume a case where the model scores around 65% in classifying the testing subset. This could mean that either the model is trained insufficiently OR that the testing subset consists of outliers. In the latter case, training the final model with them would decrease its performance and you find out only after deploying it.   Re-phrasing my initial question:     If you had a one-time demonstration of a model, such as deploying it   on embedded electronics on-board an expensive rocket experiment, would you trust a   model that has been re-trained with the test subset in the final step without being   re-tested on its new performance?