How come Naruto is in same year as Sasuke even after failing graduation 2 times?
Since Naruto failed the Genin exam so many times, doesn't that mean he's older than Sasuke and Sakura?
$r$ primitive root of prime $p$, where $p \equiv 1 \mod 4$: prove $-r$ is also a primitive root question is as follows:  Let $p$ be a prime with $p \equiv  1 \mod 4$, and $r$ be a primitive root of $p$.  Prove that $-r$ is also a primitive root of $p$.  I have shown that $-r^{\phi(p)} \equiv 1 \mod p$.  What I am having trouble showing, however, is that the order of $-r$ modulo $p$ is not some number (dividing $\phi(p)$ that is LESS than ($\phi(p)$).  By way of contradiction, I've shown that the order of $-r$ cannot be an EVEN number less than $\phi(p)$.  But my methodology does not work for the hypothetical possibility of an ODD order that is less than $\phi(p)$.  Any and all help appreciated.  Happy to show methodology for any of the parts I have managed to do, if requested. I want my prompt to display:   current (absolute) working directory, colored in green and in a NEW line, the dollar sign and an empty space.   I am using this line in .profile  export PS1='\e[0;32m$(pwd)\n\e[m$ '  So when in e.g. Desktop, my prompt looks like this:    However, sometimes when hitting the up arrow to re-run previous commands, at the start of the prompt a random char sequence appear that does not seem to go away unless I hit enter, e. g.    I have never hit a cd cd Desktop command. The weirdest part is that backspace won't even delete the first one of the two cd commands above!  Any suggestions? What is the origin of the word  as in the interjection:     — It's hot in the desert.   — Well, duh!   If it is of onomatopoeic origin and only appears in modern English as some sites suggest, I would be interested to know when it started appearing in English writing. How can I easily encrypt a file? I was given this problem 30 years ago by a coworker, posted it 15 years ago to rec.puzzles, and got a solution from Barry Wolk, but have never seen it again.  Consider the series:  $$1, \frac{1}{2},\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}},\frac{\displaystyle\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}}}{\displaystyle\frac{\displaystyle\frac{5}{6}}{\displaystyle\frac{7}{8}}},\cdots$$  Each fraction keeps its large bars while being put atop a similar structure. This can also be represented as $$\frac{1\cdot 4 \cdot 6 \cdot 7 \cdot\cdots}{2 \cdot 3 \cdot 5 \cdot 8 \cdot\cdots}$$ terminating at $2^n$ for some $n$, where it is much closer to the limit than elsewhere.  The challenge:   Find the limit, not too hard by experiment In the last expression, find a simple, nonrecursive, expression to say whether $n$ is in the numerator or denominator Prove the limit is correct-this is the hard one. What canonical momenta are the "right" ones? I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the conjugate momenta $\pi^\mu_{\ \ \ \nu} = \partial \mathscr{L} / \partial(\partial_\mu A^\nu)$, I can use two methods.  First method: directly apply this to $\mathscr{L}$. We get a a factor of $2$ since there are two $F$'s, and another factor of $2$ since each $F$ contains two $\partial_\mu A_\nu$ terms, giving $$\pi^\mu_{\ \ \ \nu} = -F^\mu_{\ \ \ \nu}.$$  Second method: get $\mathscr{L}$ in terms of $A$ by expanding and integrating by parts, yielding $$\mathscr{L} = \frac{1}{2}(\partial_\mu A^\mu)^2 - \frac{1}{2}(\partial_\mu A^\nu)^2.$$ Differentiating this gets factors of $2$ and gives $$\pi^\mu_{\ \ \ \nu} = \partial_\rho A^\rho \delta^\mu_\nu - \partial^\mu A_\nu.$$  These two answers are different! (They do give the same equations of motion, at least.) I guess that means doing the integration by parts changed the canonical momenta.  Is this something I should be worried about? In particular, I have another exercise that wants me to show that one of the canonical momenta vanishes -- this isn't true for the ones I get from the second method! Plus, my stress-energy tensor is changed too. When a problem asks for "the" canonical momenta, am I forbidden from integrating by parts? Prove that the additive groups of $\Bbb Z$ and $\Bbb Q$ are not isomorphic.    It is hard to create a map that will show homomorphism. How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$ Preamble: I know that 'give a reason when downvoting' is a very common request, and I assure you that I have read these posts and the discussions in them and my request is very different. This isn't about encouraging people to comment and is more about gathering metrics.  I'd like to see a feature whereby people who are downvoted get some better feedback on why they were downvoted, especially given that people rarely leave comments in practice.  So my suggestion is that when user clicks on the downvote, they are prompted to pick from a short list (No more than 5) of common reasons. It would be a popup that replaces the existing "Please consider adding a comment" box.  The user receiving the downvote would see how many people downvoted them for each reason, but not who did it. It would significantly address the issue of people being too lazy to comment or not wanting to comment (for fear of retaliation or any other reason) while helping to ensure the user gets useful feedback.  Perhaps the downvote could also be weighted based on whether or not a reason is picked.  For questions the list might look something like:   Not a question Not relevant to the subject area Trivial question with no research effort Poorly asked question Other   And for answers, this might be:   Nonconstructive or not an answer Incorrect or dangerous answer Poor explanation Doesn't answer the original question Other Cyberpunk/Post-Apocalyptic Sci-Fi series from the 90s or 00s based in Manhattan Replicate data from one list to another list sharepoint I have a list A with columns Emp ID, First name &amp; last name and list B wih column name Emp ID, First name, last name , phone number and address.  I want functionality such that when i enter item in List A and save same data should get copied in 3 columns of list B. Can someone help me with the approach. Thnks I need to test this code, but when writing a trigger, I get an invalid type I need help. I am currently trying to test this code before uploading  public class CoreValuesExt { ApexPages.StandardController sc; public boolean readonly {get; set;} public Core_Values__c cv {get; set;} public integer countEdit = 1; public string buttonValue {get; set;} public integer recordScan;  public CoreValuesExt(ApexPages.StandardController sc) {     this.sc = sc;     cv = new Core_Values__c();     cv.Account__c = sc.getid();      readonly = true;     buttonValue = 'Edit';     recordScan = [SELECT COUNT() FROM Core_Values__c WHERE Account__c = :cv.Account__c];    if (recordScan != 0){    cv = [SELECT id, HSE__c, Professionalism_Integrity__c, Quality_Accuracy__c, Technology_Innovation__c, Timeliness__c, Value_for_money__c FROM Core_Values__c WHERE Account__c = :cv.Account__c];     }  }  public ApexPages.PageReference Save() {     return sc.Save(); }  public void ApplyAction() {     countEdit++;     Integer modolus = Math.mod(countEdit, 2);     String total = cv.HSE__c + cv.Professionalism_Integrity__c + cv.Quality_Accuracy__c + cv.Technology_Innovation__c + cv.Value_for_Money__c + cv.Timeliness__c;     if(modolus == 0)     {         readonly = false;         buttonValue = 'Save';     }     else     {         if(total != 'nullnullnullnullnullnull')            {         if (recordScan == 0){         insert cv;         readonly = true;         buttonValue = 'Edit';         }         else         {         update cv;         readonly = true;         buttonValue = 'Edit';         }         }     }    }   }  With this trigger.  trigger CoreValuesTrigger on Core_Values__c (before insert) {  Core_Values__c cvs = Trigger.new; CoreValuesExt.ApplyAction(cvs);  }   But when I try to save, I get a message saying:      Illegal assignment from List to   CoreValuesExt__Core_Values__c at line 3 column 1   "  How do I go through with this? I need help. Thanks Much less than, what does that mean? What exactly does $\ll$ mean?  I am familiar that this symbol means much less than.   ...but what exactly does "much less than" mean? (Or the corollary, $\gg$)  On , the example they use is that $1\ll 9999999999$ But my thought on that is that $10^{10^{10^{11}}}\ll 10^{10^{10^{11}}}+9999999999$, based on the same logic. But I am confused because the numbers are comparitively.   Logically, I am really kinda spent dealing with this issue of mine. Thanks for any input. Identification of particles and anti-particles How can I customize different nodepart with different textures? My question is how can I customize hatch patterns(grid, vertical line, etc.) for different nodepart in a node?  The following is a failed try.  \documentclass[border=2mm,convert]{standalone} \usepackage{tikz} \usetikzlibrary{shapes.multipart,patterns}  \begin{document} \begin{tikzpicture} \node[rectangle split,rectangle split parts =2,rectangle split part fill={red!30,red!10}, rectangle split part pattern={grid,},draw]{one \nodepart{second}two}; \end{tikzpicture} \end{document} What is a suitable word to describe a place where two rivers meet? I've googled for a while and on some sites I've found the word "watershed" as the proposed word. Is it the word that best suits it? Find the coefficient of the term $x^2$ in $\left(x+\frac 2x\right)^{4}$ Find the coefficient of the term $x^2$ in $$\left(x+\frac 2x\right)^{4}$$   This is what I have done so far.  We know $a$ = $x$ and $b$ = $\frac2x$ and $n$ = 4  So what I have done is $4c2$ x $(x)^2$ x ($\frac2x$)$^2$  As we know that $^2$ + $^2$ = 4, and 4 is the $n$ value.  The answer is one though?  What have I done wrong?   P.S.  was the tutorial that helped me. How can I use the "signature" function in Preview on Mac Mini with no camera? I have a Mac Mini with no attached camera. I would like to use the feature of Preview that allows you to insert a signature. This relies on taking an image of your signature using an isight/facetime/webcam. I do not have on.  I do have a MacBook pro on which I use the signature function. Is there a way to copy a file from the the MacBook Pro to the Mac Mini to enable this function on the Mini? I studied the theoretical part about the Gravitational waves in General Relativity (linearization of gravity and small perturbations of the metric and so on).  But I was wondering about: since electromagnetic radiation is composed/carried by Photons (or better:the EM force), shall gravitational waves be composed/carried by Gravitons?   In the end:do gravitational waves imply the existence of gravitons? Or it's something unrelated and off topic? How to install CUDA 8.0 on Ubuntu 16.04 with Nvidia GeForce GTX 1080 I am attempting to install CUDA 8.0 within Ubuntu 16.04 for the Nvidia GeForce GTX 1080. I had CUDA 7.5 installed, but it did not appear to be compatible with the GTX 1080. I downloaded the .run installer from Nvidia's developer page, but the installation fails and outputs the following to a nvidia-installer.log     An NVIDIA kernel module 'nvidia-drm' appears to already be loaded in     your kernel.  This may be because it is in use (for example, by an X     server, a CUDA program, or the NVIDIA Persistence Daemon), but this     may also happen if your kernel was configured without support for     module unloading.  Please be sure to exit any programs that may be     using the GPU(s) before attempting to upgrade your driver.  If no     GPU-based programs are running, you know that your kernel supports     module unloading, and you still receive this message, then an error     may have occured that has corrupted an NVIDIA kernel module's usage     count, for which the simplest remedy is to reboot your computer.   I have rebooted the computer, but that did not resolve the problem. How do I unload the 'nvidia-drm' module so that I can install the 8.0 CUDA?