How do I install sketchup on ubuntu 15.10?
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I think the following is true:  If $q$ is coprime to $a$ then $a\mid (nq-1)$ for some $n\in\mathbb Z$.  I have started to first reducing $n\in\mathbb Z$ to $n\in\{1,\ldots,a-1\}$ and then considering all the cases $q = ka + j$ for $j=1,2,3,\ldots,a-1$. I stopped at $j=3$ and found that this is kinda messy. Does anyone have an elegant proof for this (maybe using some results from number theory)?  [Note: question has been generalized from prime $q\nmid a$ to $\,q$ coprime to $a$] How to select multiple files with keyboard only in windows explorer I'm studying abstract algebra for the first time.  let $F$ be a field. I learned that polynomials over field $F$ means polynomials with coefficients in $F$ (denoted by $F[x]$). But when I keep studying, I get to confused the word, 'polynomial functions from $F$ to $F$'.  Firstly, I consider this as induced functions from $F[x]$, so I guess all coefficients of these functions are in $F$. But let $F_{4}$ be a finite field consisting of four elements $\{0, 1, a, b\}$. and let $f: \{0,1\} \rightarrow \{0,1\}$ be a function defined by $$ f(x)=ax^2-ax$$ Since $\{0,1\}$ is a subfield of $F_{4}$ and $f(0)=0, f(1)=0$, I think $f$ is a example polynomial functions from $F$ to $F$ of which coefficients are not in $F$. Am I wrong? if so, please help me.  I encounter this problem while solving 'the set of all polynomial functions from $\Bbb{Z_{3}}$ to $\Bbb{Z_{3}}$ cannot possibly be isomorphic to $\Bbb{Z_{3}}[x]$'. I'm having trouble editing this file on Windows 7:  C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules\FindJNI.cmake   If I edit it in Cygwin (vi) or TextPad, those two programs see the changes, so it's getting written to disk somewhere.  But if I "type" the file in a DOS cmd shell, it looks like the file hasn't been changed at all.  One thing I noticed is that in the cmd shell, the owner is Administrators, but in Cygwin's bash shell, the owner is Dan:  C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules&gt;dir /Q FindJ*  Volume in drive C is Windows7_OS  Volume Serial Number is 92CA-8707   Directory of C:\Program Files (x86)\CMake 2.8.7\share\cmake-2.8\Modules  12/30/2011  09:45 AM             1,480 BUILTIN\Administrators FindJasper.cmake 12/30/2011  09:45 AM             7,951 BUILTIN\Administrators FindJava.cmake 12/30/2011  09:45 AM            10,632 BUILTIN\Administrators FindJNI.cmake 12/30/2011  09:45 AM             1,669 BUILTIN\Administrators FindJPEG.cmake                4 File(s)         21,732 bytes                0 Dir(s)  132,524,654,592 bytes free   Dan@home /c/Program Files (x86)/CMake 2.8.7/share/cmake-2.8/Modules $ ls -al FindJ* -rwx------+ 1 Dan            None 10636 Jan 30 13:57 FindJNI.cmake -rwx------+ 1 Administrators None  1669 Dec 30 09:45 FindJPEG.cmake -rwx------+ 1 Administrators None  1480 Dec 30 09:45 FindJasper.cmake -rwx------+ 1 Administrators None  7951 Dec 30 09:45 FindJava.cmake   How can this be?  It's like there are two different files with the same name in the same directory. I was using , implemented in scikit-learn, for my research work. But I have no good understanding of this.   Can anyone please give a simple, good explanation of one class SVM? Can Objective C determine the caller object reference at runtime (reflection)? 301 redirect instead of 404 when URL is a prefix of a post or page name? hey all! i have an odd problem with URL routing. when i request a URL that doesn't exist, e.g. , wordpress correctly returns a 404. however, if that URL is a prefix of a post or page name, it instead returns a 301 redirect to the post or page.  for example, if i have a post on 10/1/2010 named Food Post, it will return a 301 with Location:  (my permalink structure). likewise, if i have a page named Food Page, it will return a 301 with Location: .  you can see this in action on my live site,  . e.g.  redirects to  .  turning off permalinks (ie switching to "default") fixes it, for both posts and pages, but naturally i don't really want to do that.  i see this on three different installations, all wordpress 3.0.1 and apache 2.2, two ubuntu lucid/mysql 5.1 and one freebsd 7.3/mysql 5.0. i've deactivated all plugins and removed everything from my .htaccess except the lines for wordpress below, verbatim, but no luck.  RewriteEngine On RewriteBase / RewriteRule ^wordpress/index\.php$ - [L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule . /wordpress/index.php [L]   thanks in advance... How to add click event to an element? I am trying to determine the size in bytes of the contents in a VARBINARY(MAX) field in SQL Server 2005, using SQL. As I doubt there is native support for this, could it be done using CLR integration? Any ideas would be greatly appreciated. I'm working in a C++ unmanaged project.  I need to know how can I take a string like this "some data to encrypt" and get a byte[] array which I'm gonna use as the source for Encrypt.  In C# I do    for (int i = 0; i &lt; text.Length; i++)     buffer[i] = (byte)text[i];   What I need to know is how to do the same but using unmanaged C++.  Thanks! Bluetooth disappeared in Windows 10 I have a Lenovo G580 laptop. In the past, using Windows 8, I could use Bluetooth to connect to other devices.  Installing Windows&nbsp;10, Bluetooth simply disappeared. I can't find anything related to Bluetooth in the Device Manager, also in Settings → Devices.  There is no Windows&nbsp;10 Bluetooth driver for my laptop.  What can I do? With the advent of the WordPress Answers Stack Exchange site, there's undoubtedly going to be overlap.  But I just want to get some advice:  I'm a developer and I kinda hate WordPress, but have to use it occasionally. My WordPress questions are usually development ones (when I have them), and most often related to 'how WordPress handles things', which are pretty obvious in straight programming terms.  But with the WordPress layer of abstraction, they become problematic.  I find that most developers that have gone near WordPress are usually also PHP/JS/CSS/MYSQL guys who dabble with WordPress and, as a result, hangout more on SO. And theres a die hard bunch who are heavy into the WP.SE site, but generally the WP site is for people trying to muddle through the day to day operation of using WordPress and its many themes/plugin etc.    As a result, if I were to ask something pretty in-depth about writing / integrating new &amp; strange features or something, I'm talking to a much smaller group of devs than I would be on SO.  So, enough of the ramble, my question:  Should I be posting heavy development questions relating to WordPress on the WP.SE site or to SO? Can I post to both, or is cross posting frowned upon in these cases still? What are the most commonly used and basic Apache htaccess redirects? This question is here so we can offer users who are looking for information on how to make one or more common or basic redirects in Apache using the htaccess file. All future questions pertaining to finding information that is that is covered by the question should be closed as a duplication of this question. .  Whats the point in this question? The idea while not perfect is catch the most commonly asked questions regarding redirects using the  htaccess on the Apache platform either on  some type of lamp or a live server. The type of answers should be generally those that you could imagine are used by 100,000’s of sites world-wide and are constantly asked here at Pro Webmasters repeatedly over and over in various forms.  A few examples of the type of answers we are looking for:   How can I redirect non-www to www? How can I redirect a sub domain to the main domain? How can I redirect a sub folder from domain to a root or a subdomain?  How can I redirect an old URL to a new URL?   A few examples of the types of answers that we are not looking for:   Answers that do not involve a redirect. Any answers relating to NGinx, IIS or any other non-Apache platform. Answers that involve custom and complex string or query removals.   Resources for Advanced to Complex Mod_Rewrite Rules:      Please note: that this question is still in construction and may need some refining either by myself or a real moderator of Pro Webmasters, if you have any concerns or questions . Explanation of C++ FAQ's unsafe macro? My question is about $CFT_1$. Page 18 of  says that $$L={\frac{\overset{.}{Q}^2}{2} - \frac{g}{2Q^2}}\tag{1.11}$$ is the most general Lagrangian that preserves time translation and scale invariance in $CFT_1$. How does one prove that? Do I need a visa for a connecting flight to Japan? I'm going to the Philippines this October and would like to layover in Japan. I found a reasonably priced ticket with a 15-hour layover to Haneda, however, I have to transfer to Narita. Do I need a visa since I'm going to have to stay at a hotel and ride a bus to travel to Narita airport? Thank you! How to read a file without newlines? I'm using biblatex and I have it set up like this:  In my bib file I have 3 sorts of entrys, online, booklet, and book.   And in my thesis I want them printed separate like this:  \printbibliography[heading=subbibliography,title={Books},type=book, nottype=url, nottype=booklet, nottype=online] \printbibliography[heading=subbibliography,title={Websites},type=online, nottype=book, nottype=booklet, nottype=url] \printbibliography[heading=subbibliography,title={Misc},type=booklet]   For some reason this won't work, it still puts the websites where the books should be. And vice versa. The booklet thing does work though, it only shows my booklet entries there.  I recently started using biblatex so this might be a stupid question. Proof of the L'Hôpital Rule for $\frac{\infty}{\infty}$ I ask for the proof of the L'Hôpital rule for the indeterminate form $\frac{\infty}{\infty}$ utilizing the rule for the form $\frac{0}{0}$.   Theorem: Let $f,g:(a,b)\to \mathbb{R}$ be two differentiable functions such as that:  $\forall x\in(a,b)\ \ g(x)\neq 0\text{ and }g^{\prime}(x)\neq 0$ and $\lim_{x\to a^+}f(x)=\lim_{x\to a^+}g(x)=+\infty$ If the limit $$\lim_{x\to a^+}\frac{f^{\prime}(x)}{g^{\prime}(x)}$$ exists and is finite, then  $$\lim_{x\to a^+}\frac{f(x)}{g(x)}=\lim_{x\to a^+}\frac{f^{\prime}(x)}{g^{\prime}(x)}$$  My attempt:  Since $\lim_{x\to a^+}f(x)=+\infty$, $$\exists \delta&gt;0:a&lt;x&lt;a+\delta&lt;b\Rightarrow f(x)&gt;0\Rightarrow f(x)\neq 0$$  Let $F,G:(a,a+\delta)\to \mathbb{R}$, $F(x)=\frac{1}{f(x)}$, $G(x)=\frac{1}{g(x)}$. Then by the hypothesis $\lim_{x\to a^+}F(x)=\lim_{x\to a^+}G(x)=0$, $$\forall x\in(a,b)\ \ G(x)\neq 0\text{ and }G^{\prime}(x)=-\frac{1}{g^2(x)}g^{\prime}(x)\neq 0$$ The question is, does the limit $$\lim_{x\to a^+}\frac{F^{\prime}(x)}{G^{\prime}(x)}=\lim_{x\to a^+}\frac{-\frac{1}{f^2(x)}f^{\prime}(x)}{-\frac{1}{g^2(x)}g^{\prime}(X)}=\lim_{x\to a^+}\frac{g^2(x)f^{\prime}(x)}{f^2(x)g^{\prime}(x)}$$ exist?   The limit $$\lim_{x\to a^+}\frac{f^{\prime}(x)}{g^{\prime}(x)}$$ exists by the hypothesis but we don't know if the limit $\displaystyle\lim_{x\to a^+}\frac{g^2(x)}{f^2(x)}$ exists to deduce that the limit $$\lim_{x\to a^+}\frac{F^{\prime}(x)}{G^{\prime}(x)}$$ exists to use the L'Hôpital Rule for the form $\frac{0}{0}$.  EDIT: After discussing it with other users in the site, we came to the conclusion that this proof is only partial and can't logically be continued to yield the Theorem.  As a result, the rule for the $\frac{0}{0}$ form can't be used to proove the rule for the  $\frac{\infty}{\infty}$ form. Mr. Tavares and myself have already given two different proofs (with the pretty much the same main idea) of the Theorem in question using Cauchy's Mean Value Theorem. You can read them below. You can also read the proof Rudin gives for a stronger version of the Theorem (that does not suppose that $\lim_{x\to a^+}f(x)=+\infty$) in his book Principle of Meathematical Analysis. If you have any objections in either proofs please let me know. Thank you. I'm refactoring my ASP.net application from ASP.net 3.5 to 4.0. Also I'm changing the URLs to user friendly URLs /product.aspx?id=100 to /product-name/100.  All my pages are indexed by search engines and the site has already been online for 6 years. I'm planning to do 301 redirect from the old pages to the new one.  I want to make sure I won't lose the rankings and traffic.  Any suggestion how to do it properly?