In  on Hilbert's 10th problem in the March 2008 Notices of the AMS, Bjorn Poonen uses the equation  $$x^{1729}y^{1093}z^{196884} - 163xyzt^{262537412640768000} = 561$$  to suggest how deep the rabbit hole (of integer solutions to polynomial equations) goes. Clearly this is a cheeky equation. I recognize 1729 as the , 163 as the 9th (and greatest) , and 196884 as the linear coefficient in the  (and so, by Monstrous Moonshine, also 1 more than the degree of the smallest irreducible representation of the Monster group). Of course this made me curious about the others. Internet searches told me that 1093 is the smallest  and  262537412640768000 appears in the  for fast approximation of $\pi$. But all I could find out about 561 was that it's the area code of Palm Beach, FL.     What's the number-theoretic significance of 561?   Addendum: This question has been marked as a duplicate of  asking "Why is 561 the smallest Carmichael number?" This is not a duplicate of that question, since a person who has the present question (as I did when I asked it) does not know that 561 is the smallest Carmichael number.
A composite integer n is a Carmichael number if the only Fermat   witnesses for $n$ are those $a \in \mathbb Z_n^+$ which are not   coprime with $n$. The smallest example of such a number is $561 = 3 ·  11 · 17$   I think I understand the definition, but I don't quite understand why is the smallest Carmichael number is the above mentioned number. Please clarify.
Where can the viewport clipping parameters be changed? Zooming in to inspect texture details in 3D view clips some closer faces like shown in the image. It's not the camera view so changing camera settings doesn't help.   Where can the distance to the clipping plane be adjusted? After importing KML to Google Maps, point is showing in Antartica In the sentence     What’s funny is Cat’s dry humour.   Wouldn’t it be better to put a comma after “funny”:     What’s funny, is Cat’s dry humour.   This question entails a (at the time of writing) heated discussion in the . Unexpected behavior of rule matching a pattern How to create a YouTube playlist from a list of links? I have very long lists of YouTube links/bookmarks. I want to create playlists for my YouTube channel with them. Is there any way to do it automatically without having to add each individual URL to a playlist? What book has criminals wear a ring? I remember reading one of my father's books when I was younger.  It was about a guy who ended up getting in trouble with the law and was required to wear a ring that could not be removed and would shock the wearer any time they committed a crime (No matter how minor.)    The book was probably published in the early to mid 80s.  I thought the name of the book was 'The Ring', but I am unable to locate anything.  The cover had a car with a single wheel driving on a metal I-beam. How does \fontsize{}{} work? With the package anyfontsize I can use the command \fontsize{}{}. But the second argument seems to be without any effect. I read  that it is related to the line space. It doesn't work.  \documentclass{article} \usepackage{anyfontsize} \begin{document}  {\fontsize{1cm}{1cm}\selectfont First test : I need to put some text here.}  \bigskip  {\fontsize{1cm}{2cm}\selectfont Second test : I need to put some text here --- does it work?}  \end{document}     Any clue? Derivation of a generalization of Mertens' Third Theorem. One of Mertens' Theorems states $$\prod_{p\le x}(1-\frac{1}{p})\sim \frac{e^{-\gamma}}{\ln(x)}.$$ I have seen a generalized version that states  $$\prod_{m&lt;p\le x}(1-\frac{m}{p})\sim \frac{c(m)}{(\ln(x))^m},$$ where $m$ is a positive integer and $c(m)$ is a real number that depends on $m$. How can I derive this result? Is there a way to find what the values of $c(m)$ are? Thank you very much. Gauss law and electric flux Can you please explain me what is electric flux. I know it is $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$, but in many place its given flux means to flow. But how does electric field "flow"? Also if we assume its the electric field lines (can you also specify what exactly are these) are "flowing" how does $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$ give the total electric field lines passing through that area? (can you please elaborate when you explain?)  Pls. I know it shouldn't come here but there is no page for electric flux. Reason behind choosing the compensating resistor for input bias current in op amps I found the following explanation online on determining the values used for the compensating resistor:  In either case, the compensating resistor value is determined by calculating the parallel resistance value of R1 and R2. Why is the value equal to the parallel equivalent of R1 and R2? When using the Superposition Theorem to figure how much voltage drop will be produced by the inverting (-) input's bias current, we treat the bias current as though it were coming from a current source inside the op-amp and short-circuit all voltage sources (Vin and Vout). This gives two parallel paths for bias current (through R1 and through R2, both to ground). We want to duplicate the bias current's effect on the noninverting (+) input, so the resistor value we choose to insert in series with that input needs to be equal to R1 in parallel with R2.  Although it is a 'crisp' and simple explanation, I don't understand how it is true, since the current flowing through R2 won't directly go to the ground, but will probably enter the op-amp at the output (op-amp as a current sink). Also, it might go through a few more resistances before going to the ground, since Vout isn't directly connected to the ground. How to quickly and safely defrost chicken? How to disable captive portal detection? How to remove exclamation mark on Wi-Fi or signal icon in Lollipop? When connected to the Internet, the system checks if it's in a walled garden, which is simply trying to connect to Google. If it fails, in Android 5, there'll be an exclamation mark on the WiFi icon or signal icon.   In some situations, this is annoying. Say, in China, Google is blocked, the exclamation mark will always be there, which is meaningless.  How can I disable this check, and make the system assume, connected WiFi/mobile data is connected Internet? Zero integral of measurable $f$ on every interval implies $f=0$? Let $f:\mathbb{R} \rightarrow \mathbb{R}$ be a Borel measurable function, such that $\displaystyle \int_{a}^{b}f(x)dx=0$ for every $a&lt;b$ in $\mathbb{R}.$ Is it true that $f(x)=0$ for every $x\in \mathbb{R}$?  Comments: the starting point of this is to prove that the (Borel measurable) density function $f$ (if exists) of a symmetric random variable $X$ (meaning that $X,~-X$ have common cdf's) is even. If my question has a positive answer, it follows easily.   Thanks a lot for any comments! How can I make my local repository available for git-pull? Forcing a SimpleXML Object to a string, regardless of context Let's say I have some XML like this  &lt;channel&gt;   &lt;item&gt;     &lt;title&gt;This is title 1&lt;/title&gt;   &lt;/item&gt; &lt;/channel&gt;   The code below does what I want in that it outputs the title as a string  $xml = simplexml_load_string($xmlstring); echo $xml-&gt;channel-&gt;item-&gt;title;   Here's my problem.  The code below doesn't treat the title as a string in that context so I end up with a SimpleXML object in the array instead of a string.  $foo = array( $xml-&gt;channel-&gt;item-&gt;title );   I've been working around it like this  $foo = array( sprintf("%s",$xml-&gt;channel-&gt;item-&gt;title) );   but that seems ugly.  What's the best way to force a SimpleXML object to a string, regardless of context? How do I test for a mob, with a given name, in a certain location? I want to testfor a sheep, by the name of Lamb, in a certain location using coordinates.  I have already tried this:  testfor @e[x=999,y=80,z=-1034,type=Sheep,name=Lamb]   But it doesn't work. I have also tried:  testfor @e[x=999,y=80,z=-1034,type=Sheep]   But it says it found a sheep whether or not there is actually a sheep in that location. Prepositional Phrase - confused - at or in Which fuels burn the longest in Minecraft? Shortcuts in Objective-C to concatenate NSStrings Are there any shortcuts to (stringByAppendingString:) string concatenation in Objective-C, or shortcuts for working with NSString in general?  For example, I'd like to make:  NSString *myString = @"This"; NSString *test = [myString stringByAppendingString:@" is just a test"];   something more like:  string myString = "This"; string test = myString + " is just a test"; How to mount a RAM disk on startup? I'm trying to mount a RAM disk on startup with this:  /Users/Aram/Development/Tools/ramdisk.sh  diskutil erasevolume HFS+ "RamDisk" `hdiutil attach -nomount ram://800000`   com.aram.ramdisk.plist  &lt;?xml version="1.0" encoding="UTF-8"?&gt; &lt;!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"          "http://www.apple.com/DTDs/PropertyList-1.0.dtd"&gt; &lt;plist version="1.0"&gt;     &lt;dict&gt;         &lt;key&gt;Label&lt;/key&gt;         &lt;string&gt;com.aram.ramdisk&lt;/string&gt;         &lt;key&gt;ProgramArguments&lt;/key&gt;         &lt;array&gt;             &lt;string&gt;/bin/sh&lt;/string&gt;             &lt;string&gt;/Users/Aram/Development/Tools/ramdisk.sh&lt;/string&gt;         &lt;/array&gt;         &lt;key&gt;RunAtLoad&lt;/key&gt;         &lt;true/&gt;     &lt;/dict&gt; &lt;/plist&gt;   And then running:   sudo chown root:wheel /Library/LaunchDaemons/com.aram.ramdisk.plist sudo launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist   But I get these in the console:  1/08/12 1:29:25.982 PM fseventsd[64]: could not open &lt;&lt;/Volumes/RamDisk/.fseventsd/fseventsd-uuid&gt;&gt; (No such file or directory) 1/08/12 1:29:25.982 PM fseventsd[64]: log dir: /Volumes/RamDisk/.fseventsd getting new uuid: 102D7293-F1F1-4640-AA50-D547C365339F  1/08/12 1:29:24.561 PM sudo[1193]:     Aram : TTY=ttys000 ; PWD=/Library/LaunchDaemons ; USER=root ; COMMAND=/bin/launchctl load -w /Library/LaunchDaemons/com.aram.ramdisk.plist  1/08/12 1:40:17.052 PM com.apple.launchd[1]: (com.aram.ramdisk) Throttling respawn: Will start in 8 seconds   It works if I set KeepAlive to true, but then it creates a RAM disk every 10 seconds.  Is there a way to delay the script for 10 seconds before running?