Proving Kummer Theorem
highest power of prime $p$ dividing $\binom{m+n}{n}$
Regular expression to match a line that doesn't contain a word I've recently started maintaining someone else's JavaScript code. I'm fixing bugs, adding features and also trying to tidy up the code and make it more consistent.  The previous developer used two ways of declaring functions and I can't work out if there is a reason behind it or not.  The two ways are:  var functionOne = function() {     // Some code };     function functionTwo() {     // Some code }   What are the reasons for using these two different methods and what are the pros and cons of each? Is there anything that can be done with one method that can't be done with the other? When one hears that something smells, one would generally assume that it smells bad.   Isn't there a word which wouldn't bring to mind the idea of a bad odor? For example, how would you describe pot-pourri (assuming you like the smell of pot-pourri)? If possible, I would like an adjective, or a word that could takes the place of an adjective. How to mount a VirtualBox shared folder at startup? I was amused by the expression "Paid a penny and only farted" (related by @FumbleFingers), which suggested a similar Japanese saying: 大山鳴動鼠一匹 - "Find only a small mouse coming out after hearing rumblings and experiencing shaking of the big mountain."  It’s humorous. I chuckled when I read it, and I wrote to the author that I love it.  With that said, the word "fart" reminds me of another Japanese proverb, 百日の説法屁一つ- "A fart ruins 100 days of sermons by the priest", which means that a small mistake (the sound of a fart in front of the congregation) brings all his efforts to naught.  It can’t happen in big Western churches. But it could well happen in a small wooden temple where a priest would preach to 30 – 50 provincial followers. Can you imagine how the proud priest being called 'the venerable' would be embarrased when his loud fart is heard by all his followers during his serious sermon and they start to giggle here and there in the hall?  We also have a similar saying" 九仞の功を一簣に欠く, which literally means "Collapse a 9- meter sand tower with the last pile of sand."  What is the English equivalent of the saying "A fart ruins 100 days of sermons by the priest (bishop): a small mistake depreciates the value of (vitiates) all labor and effort to naught," preferably in such a humorous way? quick selection of a random row from a large table in mysql How to fill a rectangular hole with an even amount of vertices on either side? I tried crating faces but it left missing edges. In the end I was left with all the right lines but there was no vertex in the center.    Here's a follow up image in case you're wondering what I mean. Notice how there's no vertex in the center. How to test with Math.random in JavaScript? What are the colored/highlighted edges in edit mode? There are red and pink edges on my mesh.  What do these colored edges mean? How can I use them? How to normalize data to 0-1 range? I am lost in normalizing, could anyone guide me please.  I have a minimum and maximum values, say -23.89 and 7.54990767, respectively.  If I get a value of 5.6878 how can I scale this value on a scale of 0 to 1. Primary decomposition of a monomial ideal A potentially dangerous Request.Form value was detected from the client Every time a user posts something containing &lt; or &gt; in a page in my web application, I get this exception thrown.  I don't want to go into the discussion about the smartness of throwing an exception or crashing an entire web application because somebody entered a character in a text box, but I am looking for an elegant way to handle this.  Trapping the exception and showing     An error has occurred please go back and re-type your entire form again, but this time please do not use &lt;   doesn't seem professional enough to me.  Disabling post validation (validateRequest="false") will definitely avoid this error, but it will leave the page vulnerable to a number of attacks.  Ideally: When a post back occurs containing HTML restricted characters, that posted value in the Form collection will be automatically HTML encoded. So the .Text property of my text-box will be something &amp; lt; html &amp; gt;  Is there a way I can do this from a handler? While browsing Stack Overflow, I noticed that I lost a lot of reputation:        Is this serial downvoting? Will it be corrected by a rep-recalculation? How often are those done?    Here's a second instance: (I am not asking how to block my posts on my timeline.)  I am asking how I can block my activity, such as posting in open groups, making comments on people's posts, adding a friend, liking a photo, liking a post, etc., from people seeing it in their news feeds?  I don't want people seeing my interactions with other people. Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. I have been having a lot of trouble teaching myself rings, so much so that even "simple" proofs are really difficult for me. I think I am finally starting to get it, but just to be sure could some one please check this proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field. Thank you.  Proof: Notice that $$\langle 1 - i \rangle\\  \Rightarrow 1 = i\\  \Rightarrow 2 = 0.$$ Thus all elements of the form $a+ bi + \langle 1 - i \rangle$ can be rewritten as $a+ b + \langle 1 - i \rangle$. But since $2=0$ this implies that the elements that are left can be written as $1 + \langle 1 - i \rangle$ or $0 + \langle 1 - i \rangle$. Thus  $$ \mathbb Z[i]/ \langle 1 - i \rangle = \{ 0+ \langle 1 - i \rangle , 1 + \langle 1 - i \rangle\}. $$  This is obviously a commutative ring with unity and no zero-divisors, thus it is a finite integral domain, and hence is a field. $\square$ Do SAS expanders work transparently with SAS controllers? I'm new to SAS expanders and I'm trying to get things right. I understand that SAS expanders, when used with SAS controllers which supports expanders, allows you to utilise the full capacity of supported drives on a controller.  However, say I've got a SAS controller with 4 x SSF-8087 ports, which by itself would support 16 disks. I could then, as far as I understand, instead connect each of these ports to an expander to increase disk capacity.  However, will the SAS controller "see" all disks as if they were connected directly to the controller and not through an expander. Could I look at controllers as switches in a network? Would I be able to create a RAID from a disk on expander 1 and expander 3?  UPDATE:  I don't really have a specific project where I need to use SAS expanders. I'm just curious about how they work, and was thinking about how it would work if I used one or more SAS expanders with a LSI MegaRAID controller (9260-16i) which is running in one of our servers. However, I haven't really put any thought into the distinction between "local" disks and disks in another enclosure. The LSI MegaRAID controller has 4 SFF-8087 ports, which makes it capable of accomodating 16 drives. I have come across numerous questions where I am given the picture such as the above one been asked "how many rectangles are there?". I have even come across some slightly different images that instead of rectangles you are supposed to find the number of triangles. Well, I was thinking whether there is any formula or strategy that is used to solve these problems without having to manually count every shape.  Help would be appreciated.  Thank you :) Proving that an additive function $f$ is continuous if it is continuous at a single point Suppose that $f$ is continuous at $x_0$ and $f$ satisfies $f(x)+f(y)=f(x+y)$. Then how can we prove that $f$ is continuous at $x$ for all $x$? I seems to have problem doing anything with it. Thanks in advance. The program ed, a minimal text editor, cannot be exited by sending it an interrupt through using Ctrl-C, instead printing the error message "?" to the console.  Why doesn't ed just exit when it receives the interrupt?  Surely there's no reason why a cryptic error message is more useful here than just exiting.  This behavior leads many new users into the following sort of interaction:   $ ed hello ? help ? exit ? quit ? ^C ? ^C ? ? ? ^D $ su # rm -f /bin/ed    Such a tragic waste—easily avoidable if ed simply agreed to be interrupted.  Another stubborn program exhibiting similar behavior is less which also doesn't appear to have much reason to ignore C-c.  Why don't these programs just take a hint? Can I use mirroring to make a copy of my Database?