If $p > 3$ is prime, then $12 $ divides $p^2 - 1$
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
Evaluate:  $$\lim_{x\to{0}}\bigg(\frac{2}{x^3}.(\arcsin{x}-\arctan{x})\bigg)^{2/x^2}$$  I can just expand $\arcsin{x}$ and $\arctan{x}$ using their taylor expansions, but is there any other method? Privilege Notifications How can i render the reflections i see in the Look Dev viewport in Blender 2.8 i'm finding blender 2.8 confusing and i'm relatively new to blender in general anyway. While looking at my model in the Look Dev view port i can see reflections.        However, when i render my scene in eevee (and cycles), the reflections aren't rendered     Is there something i'm doing wrong or an option i haven't enabled? I'm referring to the colored circles with numbers next to them on the top of the page, to the right of my reputation counter. What do they represent? How to merge vertices in Blender? I am attempting to create my first 3D character just for practice. Being one of my first 3d models I going through the learning curve needless to say. In doing so I find myself creating many extra vertices. Where we will say 10 vertices on a rounded shape are spaced out on the equator and on the other north pole end of the edges they are very close. The close end could all be one vertex. Is it possible to say merge all points to one point and delete the rest? "I'm right, aren't I?" My dictionary reports that aren't is also an abbreviation for am not, when used in questions.  Is this use of aren't common? If it is common, are there any differences between the different English dialects?     Why aren't I being given a pay raise? Consider a text file with the following entries:  aaa bbb ccc ddd eee fff ggg hhh iii   Given a pattern (e.g. fff), I would like to grep the file above to get in the output:  all_lines except (pattern_matching_lines  U (B lines_before) U (A lines_after))   For example, if B = 2 and A = 1, the output with pattern = fff should be:  aaa bbb ccc hhh iii   How can I do this with grep or other command line tools?    Note, when I try:  grep -v 'fff'  -A1 -B2 file.txt   I don't get what I want. I instead get:  aaa bbb ccc ddd eee fff -- -- fff ggg hhh iii The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called. How can I split an equation over two (or more) lines Let $D \subset \mathbb{C}$ be the open unit disk, $f:D \to \mathbb{C}$ a holomorphic function and $d=\sup \{|f(z)-f(w)|:z,w\in D \}$. How can I show that $|f'(0)|\leq \frac{d}{2}$?  I tried using Schwarz's lemma on the function $g:D \to \mathbb{C}$ defined by $g(z)=\frac{f(z)-f(0)}{d}$, but I am only getting $|f'(0)|\leq d$. One word/phrase to describe the reaction when you eat a very spicy-hot food I've read the discussion here about .  I've also read this one: .  But I did not find any word or phrase that describes the reaction someone has when eating a too spicy-hot food. You know, they tend to sweat, catch their breath, and even sometimes shed tears; due to the spiciness of the food.  So my questions:        What do you say to describe the reaction someone has when being excitedly "suffered" by a very spicy-hot food? In Indonesian, we would call it kepedasan.   What do you say when you get that thing [the answer to question 1] with you, other than the list I enclose below:                Oh, spicy!     My God, it's spicy-hot!                      Is that it? Is there a standard idiom for comparing version numbers?  I can't just use a straight String compareTo because I don't know yet what the maximum number of point releases there will be.  I need to compare the versions and have the following hold true:  1.0 &lt; 1.1 1.0.1 &lt; 1.1 1.9 &lt; 1.10 I have a quite wide monitor and it's quite annoying to see the login dialog in the login screen on the far left side of my screen. I literally have to turn my head around to look at it!  Is there a way to center the login dialog? In the new header could we please move the chat link back to where it was? (One click away)  As a daily frequent to the JavaScript room that's the one link I'd love to have visible 100% of the time.  Aside from that, I actually love the new header. (Maybe take it a step further an add a customizable header with (X) link spots for your most used links?)  Just my thoughts How do ${0##*/} and ${0%/*} work? I'm quite confused about the following regular expressions I found in a shell script:  ${0##*/} ${0%/*}   How do they work? Windows XP INSTALL BSOD Recently I got a virus on my computer that completely wiped the hdd. I am trying to install windows xp to this: DV7-636bus laptop from HP, and I get the following BSOD:  A problem...............and Then Select Safe Mode.  Technical Information:  ***STOP: 0x0000007E (0xC0000005,0xF73B9D66,0xF78D1EA0,0xF78D1B9C)  acpi.sys - Address F72B9D66 base at F73AE000, Datestamp 480252b1   Does any one know of a solution for this? Why can't I use Stack Exchange if I'm under 13 years old, or if I'm under 16 years old and from the EU? How can the Xenomorph see? If you just look at a picture of one there are no eyes readily apparent but they clearly know where they are going. Could their screeching be some form of echo-location? Multilingual careers CVs tl/dr : Is it/will it be possible to fill out our Careers CV with localized information ?  Is it/will it possible to have different versions of the CV posted at careers (not totally different but just translated)?  Being in non English oriented country, this can be very helpful if I send local companies a link to my Careers CV and they could read it in a language other than English. LinkedIn has an implementation of this feature where you can create your profile in another language and it's up to the user to fill in the information in that language (first and last name, past experiences, etc)  The reason for this is primarily because my CV on careers contains more than just a list of bullet points, it reveals who I really am as a software developer (top tags, top answers, links to github projects, etc). Looking for a YA book about a boy that learns to use powers from an adept in a weird house that appears abandoned from the outside I am looking for a YA book about a boy who learns to use powers from a mind-adept, in a seemingly abandoned house. The adept helps him open his mind by using a cube. One of his powers, I believe, is to go into dreams of people that  he knows. He helps his young female neighbor friend by doing this, opening a door in her mind. He tries to open the mind-door of a local older bully, but finds out the young man can't be helped because he has been abused mentally and physically. I don't believe the book I read is past 1995. It might have the word "adept" in it.