What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$? What are the integer numbers $x$ such as $x^4+x^3+x^2+x+1$ is the square of an integer?  $0$ and $-1$ are obvious answers, but how many are there?
Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square. Integer values of $x$ for which $\bf{x^4+x^3+x^2+x+1}$ is a Perfect Square.  $\underline{\bf{My\; Try}}$:: Let $\bf{x^4+x^3+x^2+x+1 = k^2}$, where $k\in \mathbb{Z}$  $4x^4+4x^3+4x^2+4x+1 = 4k^2 = (2k)^2$  Now How can I proceed after that  Help Required,  Thanks
Today a student asked me $\int \ln (\sin x) \, dx.$ Calculate the integral $$\int \ln (\sin x) \, dx.$$ How can I view and examine the Android log? Capturing emoticons using regular expression in python Integrating the inverse of a function. $f(x)$ is a strictly increasing, and continuous, function on $[0,+\infty)$. Consider the integral,  $$\int_0^a f^{-1}(x) dx.$$  Reasoning  The interval $[0,a]$ is "reflected" across the line $y=x$ onto the interval $0 \leq y \leq a.$  $f(x)$ and $f^{-1}(x)$ are symmetric across the line $y=x$. So, the integral is equivalent to the area bounded by $y = 0$, $y=a$, and $f(x)$.  So, "integrating $f$ along an interval on the $y$-axis" is the same as integrating $f^{-1}$ along the same interval on the $x$-axis?  Question  Is my reasoning correct? Graphing y=x^2 and y=x I want to draw the region bounded by y=x^2 and y=x. Any ideas? I was hoping this would be somewhat simple. I've tried used a similar, with \begin{axis}..\end{axis}, but it doesn't like that. Did I not declare a package or something?   Also, if I wanted to show the solid this region creates by rotating it about the x-axis, is there a way to did this in latex? (If you had cal 2, think volume of a solid rotated about ...). I'm using NetBeans, trying to change the familiar Java coffee cup icon to a png file that I have saved in a resources directory in the jar file.  I've found many different web pages that claim they have a solution, but so far none of them work.  Here's what I have at the moment (leaving out the try-catch block):  URL url = new URL("com/xyz/resources/camera.png"); Toolkit kit = Toolkit.getDefaultToolkit(); Image img = kit.createImage(url); getFrame().setIconImage(img);   The class that contains this code is in the com.xyz package, if that makes any difference.  That class also extends JFrame.  This code is throwing a MalformedUrlException on the first line.  Anyone have a solution that works? If a question is in all-uppercase or all-lowercase, our quality filters should automatically reject it Proposal If a question on an English-language Stack Exchange site does not contain at least one uppercase and one lowercase letter, our quality filter should reject it. (We can make exceptions for sites which don't use a mixed-case alphabet, such as .) Justification The quality filter currently rejects neither all-uppercase nor all-lowercase posts. I've checked. The best Stack Exchange users use mixed case. If an asker is too lazy to use their Shift key, their question tends not to be of very good quality. Don't take my word for it. You can see proof. Sam Saffron helped me write  which lets you see with your very own eyes that what I am saying is true. Single-case askers tend to ask poor-quality questions such as:      In addition, posts which use only uppercase or only lowercase — even if they aren't riddled with typos or grammatical errors — tend to be hard to read. Capitalization aids readability. Why is this proposal not a duplicate? This proposal is not a duplicate of the older proposal . This is because it also deals with all-lowercase questions. All-lowercase questions are 50 times more common than all-caps questions.  Stack Overflow gets only about 100 all-uppercase questions per year; see .  Yet it gets about 5,000 all-lowercase questions per year; see . (These statistics are for Stack Overflow only; the rest of our network wasn't considered.) I suspect that the older proposal was declined for two reasons:  All-uppercase questions are rare.  Therefore, the effort required to block all-uppercase questions is too much.   This proposal is better. For just a bit more effort, the Stack Exchange developers can get a much richer reward. Conclusion What do you think of my proposal? Agree? Disagree? Thoughts? PS: This idea is modified and adapted from  by Stack Exchange user Gilles. My dear sir Gilles, I thank you. Note There's even a  which automatically detects questions with all-caps titles and alerts interested users and moderators. Someone found this quiver with surprisingly high values, although I'm unable to find a level 30 rare quiver on     Given that the item's internal level (IIL) determines which affixes are possible, I'd like to know whether the IIL affects the minimum/maximum rolls for an attribute, a graph or table would be great.  For example, let's say items are able to get a pure +intellect affix from IIL 20, what's stopping you from rolling 250 at 20?  Is it a bell curve, which has shallower gradients with a higher IIL of the item?  Is it capped, dependant on IIL?  Do the min/max caps step up at certain IILs,though it's the same attribute? For example, IIL 20-40 is capable of 5-120, IIL 41-60 is capable of 20-320, ..., IIL 63 = 40-400 MySQL autoincrement column jumps by 10- why? I have a couple tables in which I created an object ID as either an Int or Bigint, and in both cases, they seem to autoincrement by 10 (ie, the first insert is object ID 1, the second is object ID 11, the third is object ID 21, etc).  Two questions:   Why does it do that? Is that a problem? Looking for the name of a card-battle cartoon show Looking for a show about a group of three kids/teens who, using cards to change into monsters, fight and recover relics. I believe there are two or three other groups of three also trying to get the relics.  In the main group there are two boys and a girl. The boys were both white, one is from a farm and I don't know where the other is from. The girl was dark skinned and either black or blue hair. The three travelled around the world using a red plane.  I think they only use one monster primarily. The girl uses a monster created from gas and at one point is green. One of the boys uses a metal robot most of the time and at one point is given another better version of that card to use. I believe the episode for this was called something like green with envy.  All I'm getting from the internet is that it may be Chaotic, but that isn't the right show.  I also believe the girl's name was Mai and one of the boys were Ky, but I may be wrong. What are complex numbers, actually? Probably not with Trello, but maybe with some integration.  What I need is a solution for archiving cards because I'm not going to work with them now, but later they would come back, so I would remember doing what should be done.  Something in the lines of some email "follow up" services out there that help you remind things and at the same time keep your inbox clean. Why can't I associate files with Excel after upgrading to 2010? Under what conditions is the exponential map on a Lie algebra injective? Let $G$ be a Lie group with Lie algebra $\mathfrak{g}$ and let $\exp :\mathfrak{g}\rightarrow G$ be the exponential map.  In his blog,  that if a Lie group is not simply-connected, then $\exp$ will not be injective.  Conversely, is it true that if a Lie group is simply-connected, then $\exp$ is injective?  If not, what is a counter-example? I have the following code in my theme's archive.php:  &lt;?php the_archive_title( '&lt;h1 class="page-title"&gt;', '&lt;/h1&gt;' ); ?&gt;   This gives me titles like "Category: Russia", "Tag: America", "Author: John".  I would like to remove the "Category:", "Tag:" and "Author:" part and just display the category, tag and author names.  Does anyone know how to accomplish this?  Thank you. Pronoun immediately following its antecedent Is placing a pronoun immediately after its antecedent in a sentence valid grammar?  Is there a term for this construction?  Some examples are:   President Obama, he gave a speech last night. The speech, it was about the financial system.   I hear this on the Planet Money podcast at least once per episode. JavaScript property access: dot notation vs. brackets? I tried to fix my hard drive using Ubuntu but I encountered an error message and didn't know how to proceed. I need to fix my bad sectors   fsck /dev/sdb   fsck from util-linux 2.20.1   e2fsck 1.42.5 (29-Jul-2012)   fsck.ext2: Permission denied while trying to open /dev/sdb   You must have r/w access to the filesystem or be root How many bandits must agree? Problem  A group of $n~(1 \leq n \leq 30)$ bandits hid their stolen treasure in a room.  The treasure needs to be locked away.  The bandits want to ensure that at least $k~(1 \leq k \leq n)$ of the bandits must agree in order to retrieve the treasure.  They have decided to place multiple locks on the door such that the door can be opened if and only if all the locks are opened.  Each lock may have up to n keys, distributed to a subset of the bandits.  A group of bandits can open a particular lock if and only if someone in the group has a key to that lock.  Given $n$ and $k$, how many locks are needed such that if the keys to the locks are distributed to the bandits properly, then every group of bandits of at least size $n$ can open all the locks, and no smaller group of bandits can open all the locks?  For example, if $n=3$ and $k=2$, only 3 locks are needed - keys to lock 1 can be given to bandits 1 and 2, keys to lock 2 can be given to bandits 1 and 3, and keys to lock 3 can be given to bandits 2 and 3.  No single bandit can open all the locks, but any group of 2 bandits can open all the locks.  My thoughts  At first glance, I thought it was just a simple combinations problem ($nCr$), and the provided test cases confirmed my suspicions: when $n=3$ and $k=2$, $\binom{3}{2}=3$.  Likewise, when $n=5$ and $k=3$, $\binom{5}{3}=10$.  However, two cases where this doesn't work are where $n=2$ and $k=1$ and $n=5$, $k=4$ (it gives $2$ and $5$, respectively, when the correct answer according to the judging data should be $1$ and $10$).  Next, I bothered a colleague who's a math major, and he briefly glanced at it and suggested it might be a hypergeometric distribution problem.  However, if this is correct, I'm having trouble wrapping my head around it - all the examples I can find have 2 distinct categories, e.g. red and green marbles being drawn from an urn, and I don't see that here.  An example in the terms of this problem would be extremely helpful.  If this isn't correct, where do I go from here?  I've been spinning my wheels on it for quite a while.  Background  This is for homework for a CS class (I'm a CS major with 2 semesters of calc plus discrete).  I'd like to be able to understand the math behind it, because once I can understand it, I can program it.  This problem originally came from an ACM ICPC regional contest this year, but my professor has made it into a challenge homework problem. tar and its key letters: is it a bug or feature? I am wondering to ask the difference of these two commands (i.e. only the order of their options are different):   tar -zxvf foo.tar.gz tar -zfxv foo.tar.gz   The first one ran perfectly but the second one said:  tar: You must specify one of the `-Acdtrux' or `--test-label'  options Try `tar --help' or `tar --usage' for more information.   And tar with --test-label and -zfxv said :  tar (child): xv: Cannot open: No such file or directory tar (child): Error is not recoverable: exiting now tar: Child returned status 2 tar: Error is not recoverable: exiting now   Then I looked at tar manual and realised that all the example there are using switch -f in the end!!  AFAICT there is no need for this restriction, or is there?! because in my view switches should be order free.