What happens when a devil fruit eater is asleep?
Why does a Devil Fruit's power nullify only if the user is knocked unconscious and not when he sleeps?
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$ Show that    $$1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$$   So, I use Fermat's little theorem, that is if $p$ does not divide $a$, then $a^{p-1}$ is congruent to $1$ (mod $p$). But I'm still confused. If $1^{p-1}$ is congruent to $1$ (mod $p$), $2^{p-1}$ is congruent to $1$ (mod $p$), and $p$ does not divide $p-1$, so $(p-1)^{p-1}$ is congruent to $1$ (mod $p$). How does that equal $-1$ (mod $p$)? Combine PHP prepared statments with LIKE VHDL Transition Function Let $\sim$ denote the equivalence relation on the $n$-sphere $S^n$ defined via   $$ (x_1,\dots,x_n,x_{n+1})\sim(x_1,\dots,x_n,−x_{n+1})\:\text{ for all }\: (x_1,\dots,x_{n+1})\in S^n. $$      Show that the quotient space $S^n/\sim$ is homeomorphic to the $n$-disc $D^n$.   I know that Ii have to show that there exists a bijective function $f: (S^n/\sim) \to D^n$ that is continuous and that the pre-image $f^{-1}$ is continuous as well, but I can't advance from here, any tips? I am trying to run some unit tests in a C# Windows Forms application (Visual Studio 2005), and I get the following error:  System.IO.FileLoadException: Could not load file or assembly 'Utility, Version=1.2.0.200, Culture=neutral, PublicKeyToken=764d581291d764f7' or one of its dependencies. The located assembly's manifest definition does not match the assembly reference. (Exception from HRESULT: 0x80131040)** at x.Foo.FooGO() at x.Foo.Foo2(String groupName_) in Foo.cs:line 123 at x.Foo.UnitTests.FooTests.TestFoo() in FooTests.cs:line 98** System.IO.FileLoadException: Could not load file or assembly 'Utility, Version=1.2.0.203, Culture=neutral, PublicKeyToken=764d581291d764f7' or one of its dependencies. The located assembly's manifest definition does not match the assembly reference. (Exception from HRESULT: 0x80131040)  I look in my references, and I only have a reference to Utility version 1.2.0.203 (the other one is old). Any suggestions on how I figure out what is trying to reference this old version of this DLL file? Besides, I don't think I even have this old assembly on my hard drive. Is there any tool to search for this old versioned assembly? Tools for tracking NPC/PC relationships and attitudes I have always had difficulty keeping track of NPCs, their attitudes and their relationships with each other and the PCs. I find relationship webs/diagrams are helpful, but find them difficult to keep up to date and accurate from session to session.  Are there any tools that would help with this task? I am aware that some general mapping software exists, but am more interested in tools specifically designed for RPGs. Also, I would prefer a graphical interface if software is suggested, and to not have to learn a text based language to define the diagram. However, if it turns out that the only tools available are more generalised, and/or complex, I would still like to hear about them as answers. How do I delete data for one game in the iPad Game Center? I can't type a “b” when I'm in the command line How to use "tens of" and "hundreds of"? If I'm not mistaken, tens of means 10 to 99 and hundreds of means 100 to 999. Is this correct? I found in some dictionaries that tens of is actually not correct.  I also found that hundreds of could also mean any arbitrary large number. So how would people usually interpret hundreds of? Based on context?  In my case, I want to describe numbers of some items that are usually 50-90 but sometimes could be around 100-200, but definitely not as many as 300 or so. I want to really emphasize that there are a lot of these items. In this case, can I say "... have tens or even hundreds of ..."? Would people misinterpret what I actually want to say? How can I resolve the error "cannot execute binary file"? When I login using SSH, all I can see is this...  -bash: /usr/bin/id: cannot execute binary file -bash: [: : integer expression expected   I couldn't do anything in here. Commands such as halt, poweroff, reboot will return command not found.  How can I fix this? I am using Debian Squeeze Linux Is it appropriate to ask questions about software licenses/licensing on ? Or is the appropriate place  ? Or is there no appropriate site currently and we should suggest such a site on ? Declaring Text Decorations such as Underline, Strikethrough in a Style How do I include text decorations such as Underline, Strikethrough etc in a Style definition:  &lt;Style x:Key="UnderlinedLabel"&gt;      &lt;Setter Property="Control.FontFamily" Value="Trebuchet MS" /&gt;      &lt;Setter Property="Control.FontSize" Value="14" /&gt;      &lt;!-- Next line fails --&gt;      &lt;Setter Property="Control.TextDecorations" Value="Underline" /&gt; &lt;/Style&gt;   I'm familiar with using the following XAML to underline text:  &lt;TextBlock&gt;    &lt;Underline&gt;        Underlined text    &lt;/Underline&gt; &lt;/TextBlock&gt;   However text decoration is just another style, I want to be able to define it declaritively like FontWeight, FontSize etc.  [Update]  I was applying this style to a Label control.  This was my main problem.  It appears you can't underline text in a Label.  Change to a TextBlock (thanks gix) and all is well. Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics.  I need an clear argument that   involves the equations of motion for just the potentials $A^0$ and $\mathbf{A}$, and not the electric and magnetic fields.   includes sources $\rho$ and $\mathbf{J}$ in the equations of motion.  This is to justify the assertion that there are degrees of freedom that decouple from the rest of system. does not critically rely on quantum field theoretic arguments (although any supplementary remarks are welcome).     To illustrate the level of clarity I expect, I provide an argument in the Coulomb gauge $\nabla\cdot \mathbf{A} = 0$:  Of the four field degrees of freedom, the gauge condition $\nabla\cdot \mathbf{A} = 0$ removes one degree of freedom (the longitudinally polarized EM waves).  To show that among the remaining three degrees of freedom only two are propagating, consider the field equations of motion in the Coulomb gauge:  \begin{align} \nabla^2 A^0 &amp;= -\rho/\epsilon_0,\\ \big[\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\nabla^2\big]\mathbf{A}&amp;= \mu_0 \mathbf{J}-\nabla \frac{1}{c^2}\frac{\partial}{\partial t}A^0. \end{align}  The first equation is NOT a wave equation for $A^0$, and thus does not propagate.  The final equation IS a wave equation, and describes the propagation of two degrees of freedom (Gauss' law in first eq. can be solved, and then inserted into the second equation to show that $\mathbf{A}$ only couples to the Solenoidal part of the current). SQL comma-separated row with Group By clause Compiler error C3493: 'func' cannot be implicitly captured because no default capture mode has been specified How to fix invisible form fields in Firefox while using Adwaita Dark Theme (or any other dark theme) I have this issue with some form fields in Firefox and using the adwaita-dark theme. In some webpages where the field background is white, you cannot read the text because it is also white.   This question was edited in order to clarify that this kind of wording of the question might help people who are not familiar with what a GTK+ theme. I also thing that the wording will help to get more hits through search engines. If it's still considered a duplicate, I'll accept it. Displaying multiple fields as labels if one field is null in QGIS? I am having some issues trying to show multiple fields for a single label in QGIS. In QGIS2.6, attempting to display labels for a feature consisting of multiple fields results in an empty label if one of the fields is null. So for example, in the label expression dialog:  concat("Temp Site",'\n',"Notes",'\n',"Function")   will function normally unless one of the fields is null, then it results in no label being shown. Using the '||' operator instead in the expression dialog also results in the same behaviour:  "Temp Site" || '\n'  ||  "Notes" || '\n'  ||  "Function"   Is there a way to display the labels even if one of the fields is null? Finite ring has only zero divisors and units If a nonzero element $a$ of a ring $\mathbb{D}$ does not have a multiplicative inverse, then $a$ must be a zero divisor.   If $\mathbb{D}$ has finitely many elements, then the statement is true. However, I don't see why, as for the infinite case, 7 isn't a zero divisor only because every element $a &gt; 0$ when multiplied by a $b &gt; 0$ gives you $ab &gt; 0$ which has nothing to do with infinity or finite amounts of elements. Flying Turkish Airlines, what are credit card rules? I have return tickets flying out of SFO on Turkish airlines for the whole family. The credit card I used to book the tickets has since been replaced by the bank with a new card.   In order to board, can I present the new credit card (same name) at the checkin counter, or must I present the original credit card (which is no longer valid and has been discarded)?  By 'discarded' - I mean cut up and thrown away in trash. It was no longer valid, since it was replaced with a new card. So can I use the new card to travel on a booking that was made using the original card?    The new card has a new number; and the ticket was purchased through an agent. I try to solve this problem. I seems to come close to the end but I can't get the conclusion. Can someone help me complete my proof. Thanks          Show that the polynomial $h(x) = (x-1)(x-2)\cdots(x-n) + 1$ is irreducible over $\mathbb Z$ for all $n\ge1$ and $ n\ne4$.      Suppose $h(x) = f(x) g(x)$, then we must have $f(i)g(i) = 1$ for all $i = 1,2,...n$. So both $f(i)$ and $g(i)$ are $1$ or $-1$. In either case, $m(x) = f(x) - g(x)$ has degree smaller than $n$ and have $n$ different roots ($1,2,...,n$). So we must have $m(x) = 0$. Then $h(x) = f(x)^{2}$. So $n$ must be even. Let $n = 2k$. Because $f(x)$ has degree $k$, there are $k$ values from $\{1,2,...,2k\}$ at which $f(x)$ is $1$ and $k$ values at which $f(x)$ is $-1$.  This is where I got stuck. Hope some one can help me solve this. Thanks.