How can CloudFlare help me? CloudFlare help needed  Recently I was looking for a free CDN service. I was looking for free subscription. Someone suggested me cloudflare for this. I registered here but it seems to be complex for me to understand the matter. Please help me by telling me that how this is beneficial for me.  Sorry if any typos mistake.
CDN - Content Delivery Networks. How do they work and why would I want to use one? What exactly is a Content Delivery Network (CDN), how does it work, and why would I want to use one for my web site?  Which are the well-known CDNs out there?
There is a hint to show that if there were points in $\mathbb{Q}$, then there would exist $r,s, t \in \mathbb{Z}$ with $\gcd(r, t) = 1$ such that $2s^2 = t^4 - 17r^4$ , and then show that any prime dividing $s$ is a quadratic residue modulo $17$.  I'm stuck on the first bit - if you suppose $\left(\frac{a}{b}, \frac{c}{d}\right)$ is a point on the curve in $\mathbb{Q}$ (so $a, b, c, d \in \mathbb{Z}$) then you get to $2a^2d^4 = b^2c^4 - 17b^2d^4$, but I'm not sure where to go from here since you don't know that $b$ is a square? Book for proof writing Why can't a normal user `chown` a file? Expandably change letter case and use inside \csname, without a package I want to change the letter-case of a single character argument, and use that changed letter inside a \csname.  And I want to do it without an additional package.  For example, I want to pass a macro the letter {S}, and have it execute the macro \csname macros\endcsname, or pass it the letter {T}, and have it execute the macro \csname macrot\endcsname.    In my MWE, I show three approaches:   I didn't expect \lowercase to work, since I recall reading that it is not truly expanded until the last possible moment.  Surprisingly, it goes into an \edef okay, but it must not be truly expanded, because it breaks the \csname. I also formulated an approach where I used \numexpr to add 32 to the ASCII code of the argument and perform a \char upon that result.  Like \lowercase, it gives the appearance of being expandable, but it also fails inside the \csname. I finally achieve success with the stringstrings package.  Having written the package, I know the conversion was not pretty... essentially, it is an exhaustive 26-fold check of the form \if #1Aa\else\if #1Bb\else\if #1Cc\else...\fi\fi\fi, which has the virtue that it can be expandably placed into an \edef, and so it works.   There has to be a better way.  The MWE works only because I use the inefficiently calculated \tmp from METHOD 3 inside the \csname.  If I use \tmp from either of the two earlier methods, it breaks.  \documentclass{article} \usepackage{stringstrings} \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t} \newcommand\convert[1]{%   %MAKE THE ARGUMENT LOWER CASE   1) LOWERCASE\\   \edef\tmp{\lowercase{#1}}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   2) ASCII CONVERSION\\   \edef\tmp{\expandafter\char\numexpr`#1+32\relax}% PRETENDS TO EXPAND, BUT FAILS IN \csname   Here is the ``expanded'' conversion: \tmp\\   % OR   3) STRINGSTRINGS PACKAGE\\   \caselower[q]{#1}\def\tmp{\thestring}% WORKS BUT USES A PACKAGE   Here is the ``expanded'' conversion: \tmp\\   %   Now use it in a csname: \csname macro\tmp\endcsname% } \begin{document} \convert{S}\par \convert{T} \end{document}       SUMMARY OF ANSWERS:  I have added egreg's code snippets into this MWE to produce a document (and not just terminal output), showing the methods put forth to this point:  \documentclass{article}  %%%%%%%%%%%%%%%%%%%%%%%%%%%% L3 APPROACH  \usepackage{expl3}  \ExplSyntaxOn \cs_set_eq:NN \Xexplower \tl_expandable_lowercase:n \ExplSyntaxOff  %%%%%%%%%%%%%%%%%%%%%%%%%%%% EGREG'S LESS HACKY SOLUTION  \def\explowerchar#1{%   \ifcase\numexpr`#1-`A\relax    a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or l\or m\or    n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or y\or z\else    #1\fi }  \def\explower#1{%   \doexplowerchar#1\relax }  \def\doexplowerchar#1{%   \ifx#1\relax   \else     \explowerchar{#1}\expandafter\doexplowerchar   \fi }  %%%%%%%%%%%%%%%%%%%%%%%%%%%% STEVE'S HACKY PACKAGE APPROACH  \usepackage{stringstrings}  %%%%%%%%%%%%%%%%%%%%%%%%%%%%  \def\macros{Expandably converted an S to a s} \def\macrot{Expandably converted a T to a t}  \begin{document}  \textbf{Steve's hacky approach}  \caselower[q]{S}\csname macro\thestring\endcsname\par \caselower[q]{T}\csname macro\thestring\endcsname  \textbf{egreg's less hacky approach}  \edef\lcstring{\explowerchar{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\explower{T}}\csname macro\lcstring\endcsname  \textbf{L3 approach}  \edef\lcstring{\Xexplower{S}}\csname macro\lcstring\endcsname\par \edef\lcstring{\Xexplower{T}}\csname macro\lcstring\endcsname  \end{document} Brief Description:  I need my Ethernet card (en0) to see all traffic under 192.168.2.xxx.  However I also need to use WiFi card (en1) for all other traffic.  OS: OS X Lion    I am using a separate network location to deal with this specific use (since this is a for a robotics project that communicates via Ethernet). Ethernet (en0) had to be set up as a static IP (192.168.2.10) per the requirements for the device I am connecting to. All connections on the Ethernet card (en0) should be 192.168.2.xxx as specified above. WiFi (en1) is set up as DHCP to a router since their is no point in assigning it as a static for general purpose traffic. Ethernet (en0) is set up as priority over WiFi (en1).  I would also like to keep this under the network location preferences if at all possible since I do not require this feature to be on all the time.  I would really appreciate your help on this. No one I have talked to knows how to solve this. Can you flank with a reach weapon? The Variant: Flanking rules in the DMG (page 251) require adjacency, but is the intent that the Enemy has combatants on opposite sides and thus someone with Reach (and using the reach) could still flank even if not directly adjacent?  Looking for both RAW as well as Intent of the flanking rule. Why can't I import a SVG file from Adobe Illustrator or Inkscape? how to Query parent to child I have process in salesforce in such a way opportunity we can relate this opportunity to this lookup field parent_opportunity__c . Which relates opportunity to other parent opportunity.  I want to write a query parent to child :  select id,(select id from opportunity where parent_opportunity__c!=null) from opportunity where parent_opportunity__c=null   I have worked with different scenarios i cant able to crack it  select id,name,(select id,name from parent_opportunity__r) from opportunity this is showing error and   select id,name,(select id,name from opportunity) from parent_opportunity__c this is also error What approach should I take to establish this logical proof? I need to design a logical math proof:  Write a detailed structured proof to prove that if m and n are integers, then either 4 divides mn or else 4 does not divide n.   Hint: Think about the form of the statement.   I was thinking about first proving that either 4 should divide m or n in order for the first part to be true, then use proof by cases to prove what happened when m was 4, and another case when n was 4...  But I got stuck, what do you recommend:    This is what I got so far: Claim: (m ∈ Z ∧ n ∈ Z) => (4 | mn ˅ 4 ∤ n)  Negated claim: (m ∈ z ∧ n ∈ z) ∧ ( P(n) ∧ ¬P(mn) )  Proof by contradiction  Assume m , n ∈ z:    Assume P(n) ∧ ¬P(mn):       Then ∃ q ∈ R, n = 4q       Let q0 be such that n = 4q0       Then mn = m(4q0)       Then mn = 4(mq0)       Then ∃ q ∈ R, mn = 4q        Then 4 | mn     Then P(n) ∧ P(mn) Then (m , n ∈ z) ∧ P(n) ∧ P(mn))    I know that is wrong, how can I fix it? There are lots of questions tagged  that don't have a  response.  How do we interpret this? Is it because they are declined by default? We just have to wait for a response (the team is very busy)? Is Jeff the only one that reviews this questions?  I suppose the ones that have negative votes may (or may not) be declined by default, but there are quite a few with some to a lot upvotes that should have an official answer. Why is main() in java void? In the case of languages with a C-like syntax, we declare the main() method to return an int or float value (or void).  Is it possible to declare a non-void return type from main() in Java?  If not, then why not?  Does this mean that a Java program doesn't return any value to the OS? How is voltage always able to increase, if electrons move at the speed of light? TP-Link Archer T3U Plus USB adapter Cannot make this wireless adapter work on Ubuntu 20.04... please help. I've tried this:  and now lsusb sees the device, but still doesn't work. lsusb: Bus 002 Device 006: ID 2357:0138 TP-Link 802.11ac NIC uname -r: 5.4.0-39-generic Edit: It works on my other computer with Ubuntu 18.04 using T2U Plus driver from here:  But it does not work with Ubuntu 20.04... sudo modprobe 88x2bu: Gives nothing. modinfo 88x2bu | grep -e version -e 0138 : version:        v5.6.1_30362.20181109_COEX20180928-6a6a srcversion:     9C5282368F93050B7206C8D parm:           rtw_chip_version:int  dmesg | grep 88x2 : [ 8087.334869] 88x2bu: loading out-of-tree module taints kernel. [ 8087.336610] 88x2bu: module verification failed: signature and/or required key missing - tainting kernel [ 8087.341389] usbcore: registered new interface driver rtl88x2bu Why is the last digit of $n^5$ equal to the last digit of $n$? I was wondering why the last digit of $n^5$ is that of $n$? What's the proof and logic behind the statement? I have no idea where to start. Can someone please provide a simple proof or some general ideas about how I can figure out the proof myself? Thanks. Edge won't connect to internet, Skype for business won't screen-share, Windows Store won't update apps after Windows 10 version 1809 installed I ran into a problem after upgrading Windows 10 October 2018 to version 1809. After the Windows update I noticed the following problems with Microsoft applications:   Microsoft Edge could no longer connect to the internet even though Chrome, Firefox and IE 11 still could. Skype for Business (formerly Lync) no longer allowed me to share my screen or view another person's shared screen. The Windows Store could not connect to the internet to update apps. The Microsoft Feedback portal could no longer connect to the internet.   How can I resolve these network issues that seemed to cooincide with an upgrade to Win10 ver 1809? Unknown Column In Where Clause I'm a web designer and I'd like to make a custom wordpress theme for my upcoming blog. The template is already made in photoshop but I need a good starting point. I don't have too much experience with Wordpress but I want something that is SEO friendly which I can edit without risking getting poor search results.  I Know about Starkers and that there are other blank themes out there, but are they good for SEO? Version Control: Entire site or just pieces? I've been using git to track changes in the plugins and themes I've developed for different sites. Each plugin or theme has their own repository in whichever local install of WordPress I happen to be using for that project. This works fine when I'm just working on one solitary plugin or theme.  But when I have a local version of an entire site which is a collection of different plugins, themes, WordPress core, etc. Should I be keeping that entire directory under version control?  Is there a best practice to always have a collection of repositories for each theme/plugin, or for each client site to have one monolithic repository that includes all the code used in the project (including the latest copy of WordPress via svn.) Homeomorphism of the real line-Topology What is an quick way to create a new blank file in Lion? In Windows, one can create a new file using Right Click -> Add New -> Type of File. Is there an analogous action in Lion?  I just want to create a new blank file on my Desktop.