How I can check if the polynomial $x^4 + x^3 + x^2 + x +1$ is Irreducible or Not over $Z$ ?  Here, Eisenstein's criteria isn't applicable neither Mod P irreducible Test.  How should I proceed?
As opposed to the generic polynomial form for utilizing the Eisenstein Criterion ($a_nx^n+a_{n-1}x^{n-1}+\dots+a_0\in\mathbb{Z}[x]$ is irreducible in $\mathbb{Q}$) how do we prove that if $p$ is a prime, $x^{p-1}+x^{p-2}+\dots+x+1$ is irreducible over $\mathbb{Q}$?
Samba authentication fails How can I pass command-line arguments to a Perl program? I'm working on a Perl script. How can I pass command line parameters to it?  Example:  script.pl "string1" "string2" Why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$? I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$? Let $F,G,H$ be groups such that $F\trianglelefteq G \trianglelefteq H$.  I am asked whether we necessarily have $F\trianglelefteq H$. I think the answer is no but I cannot find any counterexample with usual groups. Is there a simple case where this property is not true? Conditional Expectation of Composite Function Preliminaries  Let $(\Omega, \mathcal{G}, \mathbb{P})$ be a complete probability space.  Let $D$ be a complete, separable, metrizable topological space with Borel $\sigma$-algebra $\mathcal{B}(D)$ (such as $D = \mathbb{R}^q$ with $\sigma$-algebra $\mathcal{B}(D) = \mathcal{B}(\mathbb{R}^d)$).  Let $\mathbb{R}$ be equipped with its canonical Borel $\sigma$-algebra $\mathcal{B}(\mathbb{R})$.  Let $g: \Omega \times D \rightarrow \mathbb{R}$ be a bounded $(\mathcal{G} \otimes \mathcal{B}(D) ) / \mathcal{B}(\mathbb{R})$-measurable function.  Let $\Pi: \Omega \rightarrow D$ be a $\mathcal{G}/\mathcal{B}(D)$-measurable random variable.  Let $H : \Omega \rightarrow \mathbb{R}$ be a $\mathcal{G}/\mathcal{B}(\mathbb{R})$-measurable random variable, defined by $$ H(\omega) := g(\omega, \Pi(\omega)).$$ Note, that, since $g$ is bounded, we have $H \in \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P})$.  Let $j: D \rightarrow \mathcal{L}^2(\Omega, \mathcal{G}, \mathbb{P}) $ be defined by $$ j(\pi)(\omega) := g(\omega, \pi)  $$  For all $\pi \in D$, let $j(\pi)$ be independent of $\Pi$.  Question  I am interested in the conditional expectation $$\mathbb{E}[H \mid \Pi] :\Omega \rightarrow \mathbb{R}$$ of $H$ with respect to $\Pi$. More specifically, I suspect that (a $\mathbb{P}$-unique version of) this condititional expectation is given by  $$ \mathbb{E}[H \mid \Pi] (\omega) = \mathbb{E}[j(\Pi(\omega))], \quad (\dagger)  $$ whereby $\mathbb{E}[j(\Pi(\omega))]$ can of course also be written as $$\mathbb{E}[j(\Pi(\omega))] = \int_{\Omega} j(\Pi(\omega))(\tilde{\omega}) d\mathbb{P}(\tilde{\omega}) . $$  How can I prove, that $(\dagger)$ is the case? I have tried, tracking the definition of conditional expectation and using Fubini, but with little success so far.  Thanks for any advice! I noticed that, for each research project, there comes a point where I have to consult the literature, and find all the previous research related to the current project.  Unfortunately, I seem to be very inefficient in my approach. I spend a lot of time digging through papers that are really interesting, but only of tangential importance to my current work, just to find the few papers that actually do similar things. (The pile of "cool paper, read when time" just keeps growing.)  Hence, I'm wondering: What is the most time efficient way to get a thorough overview of the literature in a specific niche of a field?    While searching for an answer I came across these questions:   - This question is quite similar and I liked the approach. I debated with myself if this is a duplicate, but I think it is focused more on how to be sure the search was exhaustive, whereas I'm worried about time efficiency. (Also, I'm a bit curious if things have changed since 2012.)   - The answer provides tips on how to identify what literature generally is important in a field, but I am looking for the most cost effective (least time consuming) way to do it in an area, where I know the broad literature, but not the specifics. How to read dash files How can I read a dash file from the terminal other than delimiting it with ./  For example to read a - file we can read it by   cat ./-file_name  Q: Is there an alternative way to achieve the same thing? Installing drivers for windows? $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. Finder windows just show screen artefacts On our Macbook Air (Mid-2011 11", OS X 10.9.5 Mavericks), starting a few days ago, every time we open Finder windows, the right side just shows screen artifacts/cheese. File Open dialogs in MS Word work fine - it is just the Finder windows with the problem.  Can someone help?  I have tried rebooting, and Verify Disk in Disk Utility. Neither helped. Maybe I should upgrade to El Capitan? But why would this start happening all of a sudden? The locker problem - why squares? There are 1000 lockers in a high school with 1000 students.  The    problem begins with the first student opening all 1000 lockers; next    the second student closes lockers 2,4,6,8,10 and so on to locker 1000;   the third student changes the state (opens lockers closed, closes    lockers open) on lockers 3,6,9,12,15 and so on; the fourth student    changes the state of lockers 4,8,12,16 and so on. This goes on until    every student has had a turn.      How many lockers will be open at the end?   I worked out this problem by doing it for 10 lockers. The pattern was obvious (1,4,9 remained open).It's easy to then say that 31 lockers remain open at the end. I don't quite understand why only square numbers remain open at the end. Is there some deeper reason? Override iTunes "media" keys (play, pause, etc) for Spotify? Recently, I am trying to create 3D models for my own game project. However, when I do some researches on game models, I come up with the term - game-ready models and I could not find any clear definition online. Could anyone tell me about what exactly is game-ready models and how to know if my 3D models (created by Blender mainly) is suitable for games.  From what I know by far, quad topology is preferred in Blender. However, for most of the game engine, triangle topology is preferred (Please correct me if I am wrong). Does it mean I have to manually change the models in Blender from quad topology to triangle topology before importing to the game engine?  Thanks for any helps. if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$ Show:   if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and   $$\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$$   then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$   My attempt:  let n = 1,  since $f'(x_0),g'(x_0)$ exists then The taylor polynomial exists: $$T_{f,1}(x)=f(x_0)+f'(x_0)(x-x_0), \lim_{x\to x_0} \dfrac{f(x)-T_{f,1}(x)}{(x-x_0)}=0$$  $$T_{g,1}(x)=g(x_0)+g'(x_0)(x-x_0), \lim_{x\to x_0} \dfrac{g(x)-T_{g,1}(x)}{(x-x_0)}=0$$  Then, \begin{align} \lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n} &amp; =\lim_{x\to x_0} \dfrac{f(x)-g(x)+T_{f,1}(x)-T_{f,1}(x)+T_{g,1}(x)-T_{g,1}(x)}{(x-x_0)^n}\\ &amp;=\lim_{x\to x_0} \dfrac{f(x)-g(x)+T_{f,1}(x)-T_{f,1}(x)+T_{g,1}(x)-T_{g,1}(x)}{(x-x_0)^n}\\ &amp;=\lim_{x\to x_0} \dfrac{f(x)-T_{f,1}(x)}{x-x_0}-\lim_{x\to x_0} \dfrac{g(x)-T_{g,1}(x)}{x-x_0}+\lim_{x\to x_0} \dfrac{T_{f,1}(x)-T_{g,1}(x)}{x-x_0}\\ &amp;=\lim_{x\to x_0}\dfrac{T_{f,1}(x)-T_{g,1}(x)}{x-x_0}\\ &amp;=0 \end{align}  Then, \begin{align} \lim_{x\to x_0}\dfrac{T_{f,1}(x)-T_{g,1}(x)}{x-x_0} &amp;=\lim_{x\to x_0}\dfrac{f(x_0)+f'(x_0)(x-x_0)-g(x_0)-g'(x_0)(x-x_0)}{x-x_0}\\ &amp;=\left(f(x_0)-g(x_0)\right)\lim_{x\to x_0}\dfrac{1}{x-x_0}+f'(x_0)-g'(x_0) \\&amp;=0 \end{align} I am confused because  $\lim_{x\to x_0}\dfrac{1}{x-x_0}$ does not exist. Word for someone who acts like an expert but who has very little knowledge? What is a word to describe an individual who acts like an expert in a subject area, constantly stating facts and correcting people, but who actually has very little knowledge on the subject? Bought a new battery, do I need to calibrate it? My original battery is bloated and is dying quickly after a full charge so I now bought a replacement. Do I need to calibrate this new battery using a calibration app? The set of all finite subsets of the natural numbers is countable How to change boot priority? I have a laptop with Ubuntu installed as the only OS. I also have a USB stick with a Windows 7 installation on it. I want to install Windows from the USB stick on my laptop but when I try to restart the laptop to get access to BIOS, I can't seem to find the command for it, its like it skips everything and just says Ubuntu and then takes me to the login screen.  How do I change the boot priority to USB in Ubuntu? I know this sounds like a stupid question, but I just wanted to confirm if they are the same thing. In new canon, anti-gravity is never mentioned. To make Latin-letter variables bold I can use e.g. \mathbf{a}, but while putting Greek letters or symbols such as \nabla inside \mathbf doesn't cause any errors or warnings, it also doesn't do anything else.  What is the best way to make bold math symbols, in particular Greek letters and \nabla?