I would like to ask where to ask a question like this:     I'm just curious if there are any known plans about what happens when the LLVM version numbers eventually catch up to Apple's ridiculous version numbers.  It's close if not has already happened.   Does such a question belong anywhere on the Stack Exchange network, or should I reach out to the mailing lists?
Stuff like polls, recommendations based on subjective constraints, puzzles, webcomics etc. do not belong on the serious main SE sites, where professionals should be considered at work and having just a few spare minutes ("code's compiling") to answer questions, so they should not be distracted by such things. However, I'd also like to have a home for these things still using the SE engine. For the reason I mentioned before, this needs to be a separate place though. Let's call it four.[sitename-here].com.
Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements I am attempting to prove what the title says, that $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements.  I have already proven that for any field $K$ and polynomial $f(x)$ in $K[x]$, $K[x]/\langle f(x)\rangle$ is a field if and only if $f(x)$ is irreducible in $K[x]$. So I know that $\mathbb{F}_p/\langle f(x)\rangle$ is a field for sure. Where I'm lost is figuring out how to know for sure that there are $p^n$ elements. It's fairly clear if $n\in\{ 0 ,1\}$, but I don't think induction is going to help.  I know from a proposition in class that since $F_p = \mathbb{Z}/\langle p\rangle$ and $F_p = \mathbb{Z}/\langle p\rangle$ is an integral domain, $F_p[x] = (\mathbb{Z}/\langle p\rangle)[x] = (\mathbb{Z}[x])/(\langle p\rangle[x])$, but I'm not sure whether or not that's helpful information. Is it really impossible to calculate in advance the result of throwing dice? Is there a sentence that begins with “them”? How do function pointers in C work? I need another LP-E5 type battery for my Canon 450D. Should I buy an original Canon battery or one of the many generic brands available? There are loads of cheapos on , for example.  I should add that the new battery will be added to my existing Canon battery in a battery grip.  Does anyone have any experience (good or bad) of using generic batteries? How to get the insert ID in JDBC? Does the closedness of a subgroup $H$ of $G$ imply that for $h\in H, g\in G \setminus H: hg \not \in H$?  I'm new to abstract algebra and this would appear to be a useful result. However, by definition, a subgroup is nearly closed, and I don't think this directly implies that for any element $g$ from $G$ not in $H$, the composition $gh \not \in H$.  Is this in fact a true statement? For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its eigenvectors are the principal components of the data.  I understand how to calculate $A^TA$, but I was wondering if there's an intuitive interpretation of what this matrix represents, which leads to its important role? After upgrading to Firefox 57 Quantum many website have rendering issues, such as empty frames, missing text or fonts, etc. I use Kubuntu 16.04 64 bit.  So far, I've tried:   Restarting Firefox in safe mode Disabling "hardware acceleration"   Wiping out my profile Purging Firefox and reinstalling Running Firefox from a clean user account   But nothing helped so far.  Any tips on how to solve this are much appreciated Product of path connected spaces is path connected Will product of path connected topological spaces be necessarily path connected? Why or why not?  Give me some hints. Thank you. Using the code below I add text to end of file names which are:  1.mp3 2.mp3   and should be:  1text.mp3 2text.mp3   but it changed to:  1.mp3text 2.mp3text   Code:  @ECHO ON  FOR %%A IN ("C:\Users\user123\Desktop\mp3\*.mp2") DO (     CALL :RenameFiles "%%~A" "%%~NXA" ) GOTO EOF  :RenameFiles  SET fname=%~2 SET renname=%fname=% REN "%~1" "%renname%text%" GOTO E I want to express $$\sum_{n=-\infty}^\infty \dfrac{1}{(z+n)^2+a^2}$$ in closed form. What comes to mind is the formula $$\pi\cot\pi z = \dfrac{1}{z}+\sum_{n\ne 0}\left(\dfrac{1}{z-n}+\dfrac1n\right)=\dfrac{1}{z}+\sum_{n=1}^\infty\dfrac{2z}{z^2-n^2}$$  and also $$\dfrac{\pi^2}{\sin^2\pi z}=\sum_{n=-\infty}^\infty \dfrac{1}{(z-n)^2}.$$ But neither of these gives the term $(z+n)^2+a^2$ that we want. Perhaps we can adjust somehow? Solve the recurrence $T(n) = 2T(n-1) + n$ Solve the recurrence  $T(n) = 2T(n-1) + n$ where $T(1) = 1$ and $n\ge 2$.  The final answer is $2^{n+1}-n-2$  Can anyone arrive at the solution? Changing website favicon dynamically I have a web application that's branded according to the user that's currently logged in. I'd like to change the favicon of the page to be the logo of the private label, but I'm unable to find any code or any examples of how to do this. Has anybody successfully done this before?  I'm picturing having a dozen icons in a folder, and the reference to which favicon.ico file to use is just generated dynamically along with the HTML page. Thoughts? Do not show ellipsis when not needed in search results When doing a search, the results page shows an ellipsis when it is not needed. For instance:    The message of that answer is shorter than the text overflow limit, which means the ellipsis (...) should not be shown. Input file in chapter title I cannot figure out how to import a file in a chapter title:  \chapter{\input{"Introduction.txt"}} \chapter{\texorpdfstring{\input{"Introduction.txt"}}{Introduction}}   Both of these fail with      Use of \@chapter doesn't match its definition.   Any help will be greatly appreciated. Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$ Let $a&gt;0$,$b&gt;0$ and $c&gt;0$. Prove that:    $$\dfrac{a^2+b^2}{a+b}+\dfrac{b^2+c^2}{b+c}+\dfrac{c^2+a^2}{c+a}\le \dfrac{3\left(a^2+b^2+c^2\right)}{a+b+c}.$$     $$\Leftrightarrow \frac{(a^2+b^2)(a+b+c)}{a+b}+\frac{(b^2+c^2)(a+b+c)}{b+c}+\frac{(c^2+a^2)(a+b+c)}{c+a}\leq 3(a^2+b^2+c^2)$$  $\Leftrightarrow 2(a^2+b^2+c^2)+\frac{c(a^2+b^2)}{a+b}+\frac{a(b^2+c^2)}{b+c}+\frac{b(a^2+c^2)}{a+c}\leq 3(a^2+b^2+c^2)$  $\Leftrightarrow \frac{c(a^2+b^2)}{a+b}+\frac{a(b^2+c^2)}{b+c}+\frac{b(a^2+c^2)}{a+c}\leq a^2+b^2+c^2$  $\Leftrightarrow \frac{c(a+b)^2-2abc}{a+b}+\frac{a(b+c)^2-2abc}{b+c}+\frac{b(a+c)^2-2abc}{a+c}\leq a^2+b^2+c^2$  $\Leftrightarrow 2(ab+bc+ac)\leq a^2+b^2+c^2+2abc\left(\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{a+c}\right)$  I can't continue. Help me Functions vs. patterns Mathematica won't give eigenvectors but Wolfram Alpha will? What am I doing wrong? Does Python have a ternary conditional operator?