Just curious about this one. Don't really know where to start, any help would be appreciated thanks.
Where $\phi(n)$ is the Euler phi function, how do you find all $n$ such that $\phi(n)|n$?
Is it possible to prevent DHCP service on SBS 2003 from shutting down due to rogue DHCP server? How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try. Exclusion in formation of comparative statements I was going through the topic "formation of comparative and superlative".       The rule says     When two objects are compared with each other, the latter term of comparison must exclude the former, as in "Iron is more useful than any other metal". If we say "Iron is more useful than any metal", that is the same thing as saying    "Iron is more useful than iron", since iron is itself a metal.   I am finding difficulty to relate the rule with example. I have a PC with an OEM install of Win 8 updated to 8.1.  It has 3 physical hard drives in it.  The drive where Windows is installed has a LOT of partitions on it already.    Can I install Ubuntu on a different physical hard drive than Windows, and be able to dual-boot?  I am able to boot to a live USB of Ubuntu 14.04, so I think I'm about ready to proceed.  But if I can make my installation easier by using a different physical drive, I'd like to do that. Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective Let $a\in \mathbb{R}$, $a\neq 0$, and $E=\{(x,y,z)\in \mathbb{R}^3:a+x+y+z\neq 0\}$ and $f:E\rightarrow \mathbb{R}^3$ defined by $$ f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big) $$ Show that $f$ is injective.    I've been trying to prove it directly by showing that if $f(x_1,y_1,z_1)=f(x_2,y_2,z_2)\Rightarrow$ $x_1=x_2, y_1=y_2,z_1=z_2$. But I get a system of equations which I'm find difficult to deal with. Any help would be greatly appreciated. Title bar settings missing in GNOME Tweaks on Ubuntu 20.04 I tried to move my "close, minimise and maximise" to the right + add the macOS theme to it. However, I have not been able to find any settings for that. In GNOME Tweaks > Windows the settings to put the buttons to the right are missing completely. How to handle relative urls correctly with a nginx reverse proxy Sure I'm not the first one that tried to serve a domain example.com from a example.net/bbb, but I haven't found a solution yet.  My NGINX configuration follows the  and looks something like this:  server {     listen 80;     server_name example.net;     root /path/to/aaa;      location /bbb/ {         proxy_pass http://example.com/;         proxy_set_header Host $host;         proxy_set_header X-Real-IP $remote_addr;     }      location / {         try_files $uri $uri/ /index.html;     }     location ~ \.(svg|ttf|js|css|svgz|eot|otf|woff|jpg|jpeg|gif|png|ico)$ {         access_log off;         log_not_found off;         expires max;     } }   I can manage to render the root of example.com in example.net/bbb but:  ISSUE 1  example.net/bbb/some/path doesn't work as expected and the index.html of example.net is rendered.  ISSUE 2  Any asset in example.com/assets gives 404 because the browser look for example.net/assets. Be great if I could solve this without placing absolute paths everywhere. I'm learning about private/public IPs, port forwarding and NAT, and still fail to see the answer to a simple question:  Suppose two users on the same network are communicating with a single server outside their network (say, me &amp; my wife send http requests to yahoo.com).  The server sees both users as a single public ip, and often - as in this case - communicating on the same port.  How does the router route the packets according to the two different connections? Is there any routing info inside the packet beyond ip/port?  Is there some 'session table' maintained somewhere? By whom and what exactly does it include? A TV show, from the 90's or 80's, very weird Does anyone remember a show, where:   An alien girl lives with a family She comes from the moon She is looking for a new king because their king (a giant baby) is dying Her spaceship its a VW van They had a doorframe, yes a doorframe, that could open to other alternative universes or dimentions Problems updating Python from the repositories today (Feb 25, 2021) NOTE: This is a Master Canonical Post for the issues observed on February 25, 2020.  All issues on Feb 25 relating to Python updates not found should be dupe-linked here.  Errors have been seen such as this today, February 25, 2021: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/p/python2.7/libpython2.7-minimal_2.7.17-1~18.04ubuntu1.3_amd64.deb 404 Not Found  Is there something up with the repositories? Why is the mol a fundamental physical quantity? I am starting to study physics in detail and as I read about physical quantities, I was puzzled why mol (amount of substance) is taken as a physical quantity.  A physical quantity is any quantity which we can measure and has a unit associated with it. But a mol represents the amount of substance by telling the number of particles (atoms, molecules, ions, etc.) present. So it is a pure number and numbers are dimensionless. So mol should not be considered a physical quantity.  Also, fundamental physical quantities should be independent of each other. I am wondering whether mass and mol are independent. This is so as they surely affect each other as we can evidently see while calculating the number of moles and using the mass of that sample for calculation.  So how is the mol a fundamental physical quantity and independent of mass? 1 Plot, 2 Scale/Axis Some irreducible character separates elements in different conjugacy classes Let $x$ and $y$ be elements that are not conjugate in $G$.  Then there is some irreducible character $\chi$ such that $\chi(x) \not = \chi(y)$.   Clearly the "irreducible" part isn't important, since any character can be written as the sum of irreducible characters, but I'm having trouble going beyond that.  I'd appreciate a good hint over a full answer, and I'd be most interested in a way to construct a group representation $\varphi:G \to GL(V)$ of $G$ such that the character of the representation takes different values on $x$ and $y$. A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime. When performing k-fold cross validation, I understand that you obtain the accuracy metrics by pointing all the folds except one at that one fold and make predictions, and then repeat this process $k$ times.  You can then run accuracy metrics on all of your instances (precision, recall, % classified correctly), which ought to be the same as if you calculated them each time and then averaged the result (correct me if I'm wrong).  The end result you want is a final model.  Do you average the models obtained to make your set of $k$ predictions to end up with the model that has the accuracy metrics obtained by the above method? How was this character poisoned in Warcraft? In Warcraft, towards the end of movie we observe the Guardian Medivh changing sides and starting to emit green light instead of blue. I might have missed that part or misunderstood but how exactly did he get poisoned? A mod-only section of the help center I am using the 2D Animation preset and so far every new scene I made had the same bright white background. Now my two latest scenes (created with 'copy settings') have a light grey background even though they are set to white. There's also no difference in surface, nodes or strength.  There are apparently exist different background shades with an off-white color but selecting the white one doesn't help either Where does "pay through the nose" originate? This question was , but I think that the only answer didn't quite understand the question so I thought I'd try again. I'm writing a paper in which I need to have references show up in two places:  a special list of &quot;key references&quot; in its own section, and a bibliography containing the rest of the references that were cited in the text. I thought that bibentry would do it, so the document looks something like: \documentclass[11pt]{article} \usepackage{natbib} \usepackage{bibentry} \nobibliography*  \begin{document}  \section{Amazing idea}  Chicken chicken chicken \citep{chicken:2010fj}.  Chicken chicken, chicken \citep{turkey:2010jk}.  \section{Key References}  \begin{enumerate} \item \bibentry{lemur:2009ii} \item \bibentry{gibbon:2011jk} \end{enumerate}  \bibliographystyle{apalike} \bibliography{amazing.bib} \end{document}  Unfortunately, this doesn't quite do it, as the resulting document presents the lemur and gibbon bibentry references correctly in the &quot;Key References&quot; section, but also prints them in the bibliography at the end of the document.  Ideally, the only entries in the bibliography would be the chicken and turkey \citep references.  I'd like it to look like:  Key references  Lemur, L. (2009). Lemur, 12(4):1-7. Gibbon, G. (2011). Gibbon, 135:1002-1009.  References Chicken, C. (2010). Chicken. Chicken Press, Coop. Turkey, T. (2010). Turkey, 7(4):E231.  What it actually looks like:  Key references  Lemur, L. (2009). Lemur, 12(4):1-7. Gibbon, G. (2011). Gibbon, 135:1002-1009.  References Chicken, C. (2010). Chicken. Chicken Press, Coop. Gibbon, G. (2011). Gibbon, 135:1002-1009. Lemur, L. (2009). Lemur, 12(4):1-7. Turkey, T. (2010). Turkey, 7(4):E231.  Is there any way to achieve this with the current method, or is there some other (possibly easier!?) way to do this?