Prove equality for Fibonacci sequence
Fibonacci addition law $F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$
When I press the power button a dialog opens, but I want to shutdown the system without receiving "Do you really really want to shutdown?". How can I choose a direct shutdown action on a pressed power button?   I had the same problem with the 11.04 version, but I don't remember the solution and yesterday I upgraded to Ubuntu 11.10. Change password on root user and user account If I change the password for the root user is that going to automatically change the password for the user account?   I found this link for root:    How do I change the user account password? Do ISTQB/ISEB Testing Certificates prove that someone can test? I have passed the , and to be honest, I'm pretty sure that anyone could pass that exam with a couple of days of studying. My question is are these certificates really of value to my career and should I put any effort into acquiring the ? Word for the situation of being unable to pass opposing pedestrian, as you both start to step same direction Is there a word or expression in English, which describes the situation, when you can't pass a  stranger, who is walking towards you on the street, because you both start to step the same direction?  I'm pretty sure I've heard one once. As I remember, it was including "dancing" reference, but in more specific way. The international Stack Overflow sites in Spanish, Portuguese, Russian, and Japanese seem to have a bug in their quick site descriptions (under their titles), for they all start with the word  For...  in English, instead of their respective languages As an example, the Spanish Stack Overflow site description is:  For programadores y profesionales de la informática  Obviously, this isn't something too big of a deal, but since they offer those sites in their respective languages, it would be nice if this issue were fixed. You can see this under &quot;More communities&quot; in the top bar.    You can also see this on the  page, where the descriptions begin with  Q&amp;A for... The  doesn't give me much hope, but I'm hoping it's an undocumented (and/or GNU-specific) feature. In The Winter Soldier, who did Peggy Carter say she married? When Steve Rogers visits Peggy Carter, she has a family photo on her nightstand and says that she married someone after Cap disappeared. Who did she marry? What's wrong with this query: INSERT INTO Users( weight, desiredWeight ) VALUES ( 160, 145 ) WHERE id = 1;  It works without the WHERE clause. I've seemed to have forgot my SQL. My processor is an Intel Core 2 Duo P8600 (2.40GHz). As far as I know that's a 64-bit processor - I'm a bit confused as the architecture is called AMD 64, is this a generic name given to 64-bit architectures? I've heard of x64 but can't see a release labelled with this. How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$ `--no-install-recommends` only specified packages I want to install xfce4-goodies but I don't want Midori Browser. With --no-install-recommends I don't know how to specify only Midori. I want the rest of packages. How to do that? Thanks! Formatting the union of sets In the example  $\cup^{i=1}_{\infty}F_i$   How do you get the i=1 directly below the union symbol and the infinity directly above? Let $p(x)$ be a polynomial of degree $n$ satisfying $p(x)\geq 0$ for all $x$. That is, for all $x$, $p(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0 \geq 0$, $a_n\neq 0$.  Show that $p(x)+p&#39;(x)+p&#39;&#39;(x)+\cdots+p^{(n)}(x)\geq 0$ for all $x$ where $p^{(i)}(x)$ is the $i^\text{th}$  derivative.  My interest: I know that, we can rewrite the LDE as follows  $$ p(x)+p&#39;(x)+p&#39;&#39;(x)+\cdots+p^{(n)}(x) = Lp(x) $$  where $L := I + D + D^2  + \cdots + D^{(n)}$. Can we say anything about a linear operator of this kind so that it does not change the sign of the input it takes? I can try to solve the question by writing for all the derivatives and factoring them using $p(x)$, but I think there should be a clever way of showing this by the properties of $L$. Can I figure out a solution by just looking at $L$ and the sign of $p(x)$ as in the question? Where should I look for that? Can you be sued for using publicly used images on a blog without copyright permission? Migrated question's answers can be upvoted twice by the same user was created on Server Fault, answered on Server Fault, I upvoted some of those answers on Server Fault, and then moved by consensus to Super User.  Now that the question is on Super User, I can upvote the same answers I previously upvoted on Server Fault. Clicking on a notification on Android app opens an empty feed When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1. Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra. Atiyah Macdonald, Exercise 8.3. Let $k$ be a field and $A$ a finitely generated $k$-algebra. Prove that the following are equivalent:   (1) $A$ is Artinian.   (2) $A$ is a finite $k$-algebra.   I have a question in the proof of (1$\Rightarrow$2): By using the structure theorem, we may assume that $(A,m)$ is an Artin local ring. Then $A/m$ is a finite algebraic extension of $k$ by . Since $A$ is Artinian, $m$ is the nilradical of $A$ and thus $m^n=0$ for some $n$. Thus we have a chain $A \supseteq m \supseteq m^2 \supseteq \cdots \supseteq m^n=0$. Since $A$ is Noetherian, $m$ is finitely generated and hence each $m^i/m^{i+1}$ is a finite dimensional $A/m$-vector space, hence a finite dimensional $k$-vector space.  But now how can I deduce that $A$ is a finite dimensional $k$-vector space? There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  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