We have:  $$p(x) = x^3+x+1\in\mathbb{Z}_5[x]$$  First of all, I tried to prove that there are no roots in $\mathbb{Z}_5$, so I tried all of them:  $$p(0) = 1\\p(1) = 3\\p(2) = 1\\p(3) = 1\\p(4) = 4$$ So since there are no roots, I can't reduce this polynomial to a linear polynomial times a 2nd degree one. T
I want to argue that argue that $\pi(\alpha)=\alpha^3+3\alpha+3$ is an irreducible polynomial over the finite field with 5 elements $\mathbb{F}_5$. My approach was just to check that $\pi$ has no roots in $\mathbb{F}_5$. Is this right?
How to prove that we are living in a 3+1D world? Regression for an outcome (ratio or fraction) between 0 and 1 I am thinking of building a model predicting a ratio $a/b$, where $a \le b$ and $a &gt; 0$ and $b &gt; 0$. So, the ratio would be between $0$ and $1$.  I could use linear regression, although it doesn't naturally limit to 0..1.  I have no reason to believe the relationship is linear, but of course it is often used anyway, as a simple first model.  I could use a logistic regression, although it is normally used to predict the probability of a two-state outcome, not to predict a continuous value from the range 0..1.  Knowing nothing more, would you use linear regression, logistic regression, or hidden option c? Vectorize a PNG file in Adobe Illustrator CC 2017 I need to open a white PNG shape in Illustrator. I want to convert it into vector and change the color. In CS6 is very simple to do this. Can you help me to do this in CC? Does Hilbert's $\varepsilon$-calculus have any real problem when using for incomplete systems? I know that this sounds like Strange Days, which I haven't seen, but from the Wikipedia description I don't think that's it.  I saw this back in the early-to-mid-90's on TV, pretty sure it was a premium channel. It follows a research group who develops a way to record experiences. Not thoughts, but at least the sights, sounds, smells, touch, etc. They record it onto this reel-to-reel tape, it looked striated and golden in color. The protagonist is the head of the research team.  I don't remember a great deal of the plot, but there were conspiracies surrounding the invention. The lab clown decides to give it a whirl by putting the bike-helmet-sized apparatus on his head and going out to have a little fun, in the classic wine, women, and song fashion. Once he returns, an older member of the team finds the tape and finds a section where the clown is having sex. Later on, the protagonist, who is the lead researcher, finds the older member shut up in his house seemingly for days and nearly comatose. The older researcher had the playback device over his head and is non-responsive. Worried, the protagonist removes the helmet and puts it on himself, only to find that the older researcher had snipped a few seconds of tape and had them running on a non-stop loop; the moment of orgasm for the clownish researcher. The older researcher eventually comes to and awkwardly apologizes.  I think there were also experiments in recording the sensorum of a lab monkey, and that played into the plot. I remember the plot seemed fairly thin and dull for what seemed to be a pretty neat idea. I don't desperately feel the need to watch the movie, but I'm mildly curious if my impressions would differ 20 years later now. How to get video duration, dimension and size in PHP? PrintWriter and PrintStream never throw IOExceptions Some days ago I realized that  (as well as ) never throw an IOException when writing, flushing or closing.  Instead it sets an internal flag (trouble=true) when an error occurs. It's not possible to get the exact exception, but only if there was some exception ().  My question is: why would one want to have such behavior? Isn't that bad API design? Any help would be appreciated.  If $n$ is a natural number $\ge 2$ how do I prove that any graph with $n$ vertices has at least two vertices of the same degree? Smooth rendering of bitmap fonts Run command on another(new) terminal window How to run any command in another terminal window?  Example: I opened one terminal window and if I run command like apropos editor, then it run and out-puts on that window. But I want to run same command on another terminal window (new window) instead on present window from first terminal.   Further clarification:  I need suggest-command &lt;command&gt; that open new terminal window and run mentioned &lt;command&gt; in that (newly opened) window. (where suggest-command is example of suggestion of command.)  How to do that? Do I need to take my weight off the bike to lock out the suspension? Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$ How do I view or install Ubuntu Touch apps? Lots of people have started developing Ubuntu Touch apps for the Ubuntu App Showdown and just in general, and have published them in the Click App Store.  What is the Click App Store, and how do I install apps published in it? I am trying to find the equation of characteristic curves and solution of the partial differential equation $$x\frac{\partial u}{\partial y}-y\frac{\partial u}{\partial x}=u$$ $u(x,0)=\sin(\frac{\pi}{4}x)$ .   What I did: $$\frac{dx}{-y}=\frac{dy}{x}=\frac{du}{u}$$ with  From first two equalities $$\frac{dx}{-y}=\frac{dy}{x}$$ by solving we get $x^2+y^2=c_1$ for some constant $c_1$. Now I am stuck with the third and rest of the equalities to come up with a suitable manipulation to solve the problem. How can I do this? Any help would be great. Thanks. I just broke the screen of my (unrooted) Galaxy S.  How do I get back my SMS and contacts?   PS: I tried Kies but it won't detect my phone for some reason. (Kies works fine with another Galaxy I possess but not this one) I've been using the Linksys USB6300 Adapter but when I switched to Ubuntu it stopped working since its only compatible with Windows. I've tried using ndiswrapper and although it says my windows driver is installed, my device isn't showing up. Anyone know how I could get this wireless network adapter working? Thanks.  lsusb  Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub Bus 001 Device 012: ID 05c6:6766 Qualcomm, Inc.  Bus 001 Device 006: ID 0bda:0153 Realtek Semiconductor Corp. Mass Storage Device Bus 001 Device 005: ID 05e3:0608 Genesys Logic, Inc. USB-2.0 4-Port HUB Bus 001 Device 004: ID 04ca:007d Lite-On Technology Corp.  Bus 001 Device 003: ID 04ca:008a Lite-On Technology Corp.  Bus 001 Device 010: ID 13b1:003f Linksys  Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub Is "performance" singular or also plural? Reset post score to 0 on migration I use Kali Linux and discovered the following "problem":  root@kali:/proc/self# ls -l cmdline -r--r--r-- l root root 0 May 27 13:43 cmdline root@kali:/proc/self# chmod 744 cmdline chmod: changing permissions of `cmdline': Operation not permitted   I am not allowed to change the permissions of that file... but I am root? Why is that? Are there ways to work around this? I allready tried some things like moving the file (what is obviously not possible), change the runlevel etc. I'll be at my uncle's house just in case you need to reach me.      I'll be at my uncle's house should you need to reach me.   Could you tell me what is the difference between those?