Show that if n divides a single Fibonacci number., then it will divide infinitely many Fibonacci numbers.
Divisibility and the Fibonacci sequence
What is the use for non-inverting input resistance in a negative feedback opamp? Here in the Figure R5=50K. This resistor value is not in the equations to obtain output voltage, and in many tutorials non-inverting input is directly grounded without a resistor. What might be the reason to use it here? The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a far-away-observer.  If this is the case how can anything ever fall into a black hole.  In my thought experiment I am in a spaceship with a powerful telescope that can detect light at a wide range of wavelengths.  I have it focused on the black hole and watch as a large rock approaches the event horizon.  Am I correct in saying that from my far-away-position the rock would freeze outside the event horizon and would never pass it? If this is the case how can a black hole ever consume any material, let alone grow to millions of solar masses.  If I was able to train the telescope onto the black hole for millions of years would I still see the rock at the edge of the event horizon?  I am getting ready for the response of the object would slowly fade.  Why would it slowly fade and if it would how long would this fading take?  If it is going to red shift at some point would the red shifting not slow down to a standstill? This question has been bugging me for years!  OK - just an edit based on responses so far.  Again, please keep thinking from an observers point of view.  If observers see objects slowly fade and slowly disappear as they approach the event horizon would that mean that over time the event horizon would be "lumpy" with objects invisible, but not passed through?  We should be able to detect the "lumpiness" should we not through? What is a catchy word that means (non-)self-descriptive I'm having fun with paradoxes, and I'm trying to come up with a catchy word for non-self-descriptive.  Maybe "autosemantic" fits the bill for self-descriptive (definitely open to other suggestions!), but I'm having a hard time negating it in a natural way.  For an example of the sentence I'm trying to construct:     Is "inautosemantic" inautosemantic?   It just isn't flowing. install ubuntu on thinkpad T440p Is there anybody, who is able to install and fully configure Ubuntu 12.04 or 14.04 on Thinkpad T440p (ver 20AN)? If yes, could you post here your procedure step by step?  Please does not include your experience with any other ThinkPad models.  Edit: Situation is not so simple, see: The sign in the formula for the voltage across the inductor This question is about voltage induced in a inductance.  I know the rate of change of current induces EMF in the inductor. The direction of the induced EMF will be opposite to the change that is causing it. The EMF induced is given by the following formula.  $$V_l = -L \frac{dI}{dt}$$  The negative sign indicates direction of induced emf across the coil is opposite the current change.     In the picture I have drawn current direction and \$V_l\$ direction.  If \$\dfrac{dI}{dt}\$ is postive, \$V_l\$ will be negative according to formula right? Or does the direction of \$V_l\$ has to be reversed?  In many Internet references I found \$V_l = L \dfrac{dI}{dt}\$. Which one is correct?  I hope they reversed \$V_l\$ reference points and removed the negative sign in the formula. Please clarify. A lot of missing dependencies when I try to install all software I have problem with missing dependencies, when I try to install some software by apt-get and also from downloaded .deb files.  I am using Debian 10. After installation I removed a lot of software which I no needed eg. Deluge, some terminals (I have only LXTerminal now), some tools from Libre Office Packet etc.  Now, when I try to install Atom, TeamViewer, or some RDP tools, every time I got information about missing unresolved dependencies, common it is libgconf, libcurl etc.  How can I resolve this issue? Now I can not install a lot of must have software, and when I try to apt-get install this packets, I got error, that no libs with this name were found.  Here is my sources.list. Maybe it will be some tip to fix this problem:  deb http://security.debian.org/debian-security/ buster/updates non-free contrib main deb-src  deb-src http://security.debian.org/debian-security/ buster/updates non-free contrib main deb-src   deb http://deb.debian.org/debian/ buster-backports main contrib non-free  deb-src http://deb.debian.org/debian/ buster-backports non-free contrib main   deb http://ftp.de.debian.org/debian stretch main contrib non-free deb-src http://ftp.de.debian.org/debian stretch main contrib non-free   Stretch repos were added for test purposes, but when I comment them, it looks the same. A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$ A closed subset of an algebraic group which contains $e$ and is closed under taking products is a subgroup of $G$.   Denote this set as $X$. If the condition of $X$ being closed is dropped, this statement does not hold. The set of nonzero integers in $\mathbb{G}_m$ over $\mathbb{C}$ is a counterexample.  It suffice to prove that for any $x \in X$, $x^{-1}X = X$. As $X$ is closed under taking products, it is clear that $X \subseteq x^{-1}X$. In order to prove the inverse inclusion, the closedness of $X$ (under Zariski topology) must be used.   Let $\phi: G \rightarrow G, y \mapsto x^{-1}y$ is a homoemorphism of $G$ as an algebraic variety. So $x^{-1}X = \phi(X)$ is a closed subset of $G$ containing $X$. But Why are they equal?  Thanks very much. accessing loop variable within a loop How to find out the terminal command of an application? I want to use some applications shown on the Unity Launcher in a terminal, but I need to know the appropriate command to run them. How can I achieve that? Show that any prime ideal from such a ring is maximal. Let R be a commutative ring with an identity such that for all $r\in$ R, there exists some $n&gt;1$ such that $r^n = r$. Show that any prime ideal is  maximal. (Atiyah and MacDonald, Introduction to Commutative Algebra, Chapter 1, Exercise 7.)    Any hints? How do you set the expiry date or a maximum age in the HTTP headers for static resources in IIS Horizontal line of custom length like an — Over the years I have slowly developed a  that validates MOST email addresses correctly, assuming they don't use an IP address as the server part.  I use it in several PHP programs, and it works most of the time.  However, from time to time I get contacted by someone that is having trouble with a site that uses it, and I end up having to make some adjustment (most recently I realized that I wasn't allowing 4-character TLDs).  What is the best regular expression you have or have seen for validating emails?  I've seen several solutions that use functions that use several shorter expressions, but I'd rather have one long complex expression in a simple function instead of several short expression in a more complex function. Can I use my single entry Schengen visa to go to a different Schengen country than originally planned? My friends and I planned to visit Germany, so I got a single entry tourist Schengen visa to Germany. However, my travel plans have changed since then, because my friends are going to Italy instead. I don't have time to apply for a visa to Italy, but I have been told that I can use my Schengen visa to enter Italy. Is that true? This started to happen immediately after I had rebooted the first time after doing a system upgrade. It first starts with a dialogue that says "System program problem detected". Then when I try to hit 'report problem' not much happens. I am led through a dialogue that always ends up the problem cannot be solved.  I am aware this is not a lot of information, however I'm not sure which information I need to publish and how should I obtain it to debug this problem.  Here's a screenshot! mysqli::query(): Couldn't fetch mysqli Which is the correct tense to use with 'by'? I gave him the money by 6 PM.   I had given him the money by 6 PM.   I can't spot the difference between them and both seem right, but I was told the first one is wrong. Can anyone say, why?  Here is a another set of sentences with the same issue:     By 5 PM I gave him the book.   By 5 PM I had given him the book.   In both the sentences the book was given before 5 PM and no later than 5 PM. But I can't understand then what the difference between them is.   Is it right to use simple past with 'by' at all? If yes, then why and if not, then why is it incorrect to use simple past with 'by'? How can I install Ubuntu without removing Windows? I need my pre-installed version of Windows 7 (or any other version of Windows), how could I install Ubuntu without erasing it? When at home I use my 13" MacBook Pro hooked up to an 27" external monitor. When working on my 27" screen I prefer to have a visible dock at all times. I have enough screen real estate to afford this luxury.  When I'm on the road working on my 13" screen I prefer to automatically hide the dock as it really gets in the way when screen real estate is limited.  I now manually switch between enabling and disabling hiding (using ⌥⌘D) but I would prefer this to happen automatically. Can I enable hiding the dock on my MacBook monitor and disable hiding the dock on my external monitor? How do I install the ubuntu-restricted-extras package?