$2^p -1$ then $p$ is a prime
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
How do I change the plymouth bootscreen? With regards to Plymouth --  Are there alternative boot screens available?  What's the easiest way to change the boot screen? Recovering user files with a Live CD I want to enable gzip compression for acethehimalaya.com. Can anybody please tell me what is the best way of achieving compression in an Apache Webserver? How to set edge bevel weights from a python script I need to set weights for some edges from a python script. I have tried looping through object.data.edges and setting bevel_weight values but I can't get it right. It only works if I have first edited some edge's bevel weight by hand from the 3d-view's transform window. But I would like to get it work from my script without any manual hacking.  Steps to reproduce:  Start Blender with default cube and switch to Scripting view.  Try to set weights for all edges:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   Verify that values changed:  for edge in C.object.data.edges:     edge.bevel_weight   Switch into edit mode in 3d-view and open up transform window by pressing n. Select edges to see that the change did not work (bevel weights are all zero). Switch back to object mode and read values again in scripting console to see that they were reset to zero:  for edge in C.object.data.edges:     edge.bevel_weight   Go back to edit mode and change some edge bevel weight straight from the transform window by hand. Go back to object mode and change values again from the scripting console:  for edge in C.object.data.edges:     edge.bevel_weight = 1.0   This time it works, bevel weights are 1.0 when you go back to edit mode and look from the transform window.   Any ideas? My final need is to apply a bevel modifier to only some set of edges and that's why I'm trying to mark them by using weights. Using vertex group for bevel modifier does not work in my situation, since I need to specify edges, not vertices, which to bevel.   I'm using Blender v2.71. Adverb-adjective compound premodifier with or without hyphen? Remarkably low condensation temperature  or  Remarkably-low condensation temperature?  The focus of remarkable is that it is such a low temperature. We are having an office disagreement and any help is much appreciated. I am trying to prove  $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$  This problem is a classic, but I seem to be missing one step or the understanding of two steps which I will outline below.   $$I_n := \int\cos^n x \ dx = \int\cos^{n-1} x \cos x \ dx \tag{1}$$  First question: why rewrite the original instead of immediately integrating by parts of $\int \cos^n x \ dx$?  Integrate by parts with $$u = \cos^{n-1} x, dv = \cos x \ dx \implies du = (n-1)\cos^{n-2} x \cdot -\sin x, v = \sin x$$  which leads to  $$I_n = \sin x \ \cos^{n-1} x +\int\sin^2 x (n-1) \ \cos^{n-2} x \ dx \tag{2}$$  Since $(n-1)$ is a constant, we can throw it out front of the integral:  $$I_n = \sin x \ \cos^{n-1} x +(n-1)\int\sin^2 x \ \cos^{n-2} x \ dx\tag{3}$$  I can transform the integral a bit because $\sin^2 x + cos^2 x = 1 \implies \sin^2 x = 1-\cos^2 x$  $$I_n = \sin x \ \cos^{n-1} x + (n-1)\int(1-\cos^2 x) \ \cos^{n-2} x \ dx \tag{4}$$  According to Wikipedia as noted , this simplifies to:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) \int \cos^{n-2} x \ dx - (n-1)\int(\cos^n x) \ dx \tag{5}$$  Question 2: How did they simplify the integral of $\int(1-\cos^2 x) \ dx$ to $\int(\cos^n x) \ dx$?  Assuming knowledge of equation 5, I see how to rewrite it as  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x  - (n-1) I_{n} \tag{6}$$  and solve for $I_n$. I had tried exploiting the fact that  $$\cos^2 x = \frac{1}{2} \cos(2x) + \frac{1}{2} $$  and trying to deal with $\int 1 \ dx - \int \frac{1}{2} \cos (2x) + \frac{1}{2} \ dx$  which left me with $\frac{x}{2} - \frac{1}{4} \sin(2x)$ after integrating those pieces. Putting it all together I have:  $$I_n = \sin x \ \cos^{n-1} x + (n-1) I_{n-2} x \left(-(n-1) (\frac{x}{2} - \frac{1}{4} \sin 2x) \right) \tag{7}$$  but I'm unsure how to write the last few terms as an expression of $I_{something}$ to get it to match the usual reduction formula of   $$\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$$ How to prove that if A, B, C are submodules of M module then $$ A \cap (B+C) = (A\cap B)+C \iff C \subseteq A $$  Any help would be appreciated! Are C++ enums signed or unsigned? And by extension is it safe to validate an input by checking that it is &lt;= your max value, and leave out >= your min value (assuming you started at 0 and incremented by 1)? Generalization of Hölder inequality What is the meaning of the third derivative of a function at a point Finite order endomorphisms Why the finite order endomorphisms are diagonalizable over the complex numbers (or any algebraically closed field where the characteristic of the field does not divide the order of the endomorphism) with roots of unity on the diagonal? I think the single dashes (hyphens) should be placed between the numbers and units in this sentence:     ...in a cylinder of 3-inch radius and 24-inch length.   Is that correct and should hyphens be added to this second sentence?     ...making a trench nearly 15 feet wide and more than 30 feet long. Gauss's Law with Moving Charges I am under DDoS. What can I do? This is a  about DoS and DDoS mitigation.   I found a massive traffic spike on a website that I host today; I am getting thousands of connections a second and I see I'm using all 100Mbps of my available bandwidth.  Nobody can access my site because all the requests time out, and I can't even log into the server because SSH times out too!  This has happened a couple times before, and each time it's lasted a couple hours and gone away on its own.  Occasionally, my website has another distinct but related problem: my server's load average (which is usually around .25) rockets up to 20 or more and nobody can access my site just the same as the other case.  It also goes away after a few hours.  Restarting my server doesn't help; what can I do to make my site accessible again, and what is happening?  Relatedly, I found once that for a day or two, every time I started my service, it got a connection from a particular IP address and then crashed.  As soon as I started it up again, this happened again and it crashed again.  How is that similar, and what can I do about it? Computer wont boot to windows I recently installed a Linux operating  system (backtrack 5 r3) I couldn't connect to the internet with it so I removed the partition manually. After that, whenever I turn on my computer it goes to a command line that says "error no File-system found" "Grub Rescue/"  I have tried f12 and booted into all the options. I also put Ubuntu 12.04 on my flash drive and tried installing it on the computer, the installation failed saying "No Available Space"  My hard-drive is 500g with about 250 left. I put the hard drive in another computer (as a secondary just to see the files. It had 2 partitions a main and one with 1 gig. I formatted it with no difference.  My Problem: I can't boot into Windows Monitor hard drive changes to files Several months ago I saw someone using an application that showed him files on the computer being modified in real time.  Basically there was an application that wasn't working correctly, so he installed the program, ran the application, and saw all the various files that the application either read from or wrote to.  He found out the application was writing a large debugging file it shouldn't be, which ended up being the problem.  I don't remember the application or the name of the person who used it, but I believe it's a freeware application.  Does anyone know what this program might be? irrationality of $\sqrt{2}^{\sqrt{2}}$. The fact that there exists irrational number $a,b$ such that $a^b$ is rational is proved by the law of excluded middle, but I read somewhere that irrationality of $\sqrt{2}^{\sqrt{2}}$ is proved constructively. Do you know the proof? Some movies feature child characters put in violent situations. This can range from crude language to extreme horror (e.g. torture, gore, etc.). As an example,  and its sequel has plenty of those scenes. It looks like a paradox that children can be actors in movies that are definitely not for children.  Do the directors usually try and avoid exposing the very young actors to the violence of such scenes, e.g. by clever dubbing and editing? Are there laws that require them to do so, just like there are ratings that prevent children from seeing some movies? In mathematics, we like talking about idempotent matrices. In a masters program that I am currently enrolled in, I have heard one professor pronounce it one way, and another professor pronounce it another way. The  explains it better than I could:  Is there a correct pronunciation for idempotent? Is it like omnipotent (om-nip-o-tent), so id-EMP-o-tent, or is it more like the two seperate words idem + potent I'd say EYE-dm-POT-nt, but then I speak Brit. Charles Matthews 07:57, 30 Jun 2004 (UTC) Ditto, but then I speak Australian ;) Dysprosia 08:01, 30 Jun 2004 (UTC) Actually the British is more like EYE-dm-PO-tnt, I guess. Charles Matthews I'd just like to pedantically point out that it would be pronounced i-DEM-po-tent because because syllable onsets are maximized. daesotho 20:33, 21 Oct 2004 (UTC) The American pronunciation puts primary stress on the second syllable ('dem') and secondary stress on the fourth syllable ('tence'). Could somebody more familiar with IPA than I am please add this to the article as an accepted pronunciation? My American dictionary says |ˈīdemˌpōtənt| for the adjective. I speak American (non-natively) and I wouldn't stress the second syllable for itempotence. My only question is, right now it says /ˌaɪdɪmˈpoʊtəns/ -- but can't it be stressed on the first syllable too? Should we add /'aɪdɪmˌpoʊtəns/ as an alternative? -- 87.160.141.177 (talk) 14:50, 3 June 2011 (UTC) And by the way I think it's silly giving a pronounciation guide as this is just imposing a particular accent. (For what it's worth I pronounce idempotent with a short 'i', as in the word 'id'). Alex Selby I agree with Alex Selby - the pronunciation guide should be extended to show the variation, or removed. Strictly, there's no reason for the first i to be long (neuter idem has a short first syllable in Latin), and I can't find any authoritative source which advocates the pronunciation given. Ms7821 (talk) 22:59, 15 July 2015 (UTC)  Is there a &quot;correct&quot; pronunciation for this word? Why is a subgroup with the index of 2 normal to the group?  I believe it has something to do with it being half and having nowhere to go.