"Show that if $\;(a, b) = 1\;$, $\;a|c\;$ and $\;b|c$, then $(a · b)|c$." $$$$Show: We know that $$x\mid w \;\;\text{and}\;\; y\mid w \Longleftrightarrow \frac{x\cdot y}{(x,y)}\mid w$$So if$$a\mid c\;\;\text{and}\;\;b\mid c\Longrightarrow\frac{a\cdot b}{(a,b)}\mid c\Longrightarrow \frac{(a\cdot b)}{1}\mid c\Longrightarrow(a\cdot b)\mid c$$$\blacksquare$$$$$*Statement correct?*
Using divisibility theorems, prove that if $\gcd(a,b)=1$ and $a|c$ and $b|c$, then $ab|c$.   This is pretty clear by UPF, but I'm having some trouble proving it using divisibility theorems. I was looking at , and if this could be proven, then the solution would follow immediately.
I am seeking advice on which memory to use with my motherboard and CPU. Below are my components and some relevant information extracted from their official websites.   NOTE: Although this is a very specific case, a general answer is equally good for me — and also alot more useful for everyone else!  CPU: AMD Phenom II X4 810   ASUS M4A785TD-V EVO listed as one of many  motherboards.   Motherboard: ASUS M4A785TD-V EVO   4 x DIMM, Max. 16 GB, DDR3 1800(O.C.)*/1600(O.C.)/1333/1066/800 ECC,Non-ECC,Un-buffered Memory Dual Channel memory architecture (Complete list of specs: ).   NOTE II: I wouldn't want to do any overclocking as I have no experience with that. So I think the 1333 MHz is the most appropriate. Since the higher frequencies are marked with "O.C."  Questions:   How can I be certain that a specific RAM will work well (or not work) together with my CPU and motherboard? (The Qualified Vendor List is a good starting point, but it's a bit limited and sometimes a bit outdated). Is it true that choice of memory is not independent of the processor? How?    I'm worried I'll be missing something essential when buying my next RAM chips :) Ubuntu 14.04 has visual artifacts and freezes I suspect that some bug makes internal linking count towards Publicity badges too. The badges :  These badges are specifically for linking to questions like the description says. The link must be clicked from outside the network in order for it to count for this purpose.  However, 2 days ago I was  for a question that I really feel does not need such linking to start with: . Also, I always try to use full links. And above all:  for the link gives me a single hit, for . Maybe it's thinking that empty REFERER headers (for those that block that, or for Safari users who ) should be counted too? Or maybe some search bot is using lots of IP addresses? Or visitors of Stack Overflow clones are to blame? Why is the detection of gravitational waves so significant? LIGO has announced the detection of gravitational waves on 11 Feb, 2016. I was wondering why the detection of gravitational waves was so significant?   I know it is another confirmation of general relativity (GR), but I thought we had already confirmed GR beyond much doubt. What extra stuff would finding gravitational waves teach us? Is the detection of gravitational waves significant in and of itself, or is there data which can be extracted from the waves which will be more useful? How to nest code within a list using Markdown Schengen Business visa without a business invitation letter What's a big-vocabulary word for someone with a big vocabulary?  I'd like to say I'm looking for a "_____". How to delete an element from an array in C# Lets say I have this array,  int[] numbers = {1, 3, 4, 9, 2};   How can I delete an element by "name"? , lets say number 4?  Even ArrayList didn't help to delete?  string strNumbers = " 1, 3, 4, 9, 2"; ArrayList numbers = new ArrayList(strNumbers.Split(new char[] { ',' })); numbers.RemoveAt(numbers.IndexOf(4)); foreach (var n in numbers) {     Response.Write(n); } Have there been any recent attempts to falsify the  hypothesis alternative to the Doppler shift explanation for the red shift, or is it simply ignored like the pilot wave quantum mechanical hypothesis alternative to the Copenhagen hypothesis of quantum mechanics has been? What new evidence would it take to get the tired light hypothesis for the red shift reexamined as the recent fluid dynamics oil drop experiments have done for the pilot wave hypothesis of quantum mechanics? Finding the closest Geometry in PostGIS What determines color -- wavelength or frequency? What determines the color of light -- is it the wavelength of the light or the frequency?  (i.e. If you put light through a medium other than air, in order to keep its color the same, which one would you need to keep constant: the wavelength or the frequency?) I need to use a metaheuristic algorithm to solve an optimization problem on a Python codebase.  Metaheuristics usually need to be written in C++ or Java as they involve a lot of iterations, while Python is weak from this point of view.  Questions:   do any Python metaheuristic packages which wrap faster languages as C++/Java exist? do any Python metaheuristic packages based on maybe cython on numba exist? other solutions? What is the C# equivalent of NaN or IsNumeric? First order differential equations with 2 varriables Does anybody know how to solve the following differntial equation?  $$w^2\cdot r+\frac{dw}{dt}\cdot r+\frac{dr}{dt}\cdot w=3g$$  where w and r are a function of time so $w(t)$ and $r(t)$. $g$ is a constant  EDIT: This equation came from a thought problem of mine which I will now explain since I still do not know how to approach the problem.  Basically I want to design a spiral track in which a vehicle will accelerate. However the total acceleration needs to be constant.   The vehicle will have 2 acceleration components, a radial component ($a_r$) and a change in speed component ($a_s$). Since we want constant acceleration: $a_r + a_s = constant$  From circular motion we know that $a_r = \omega ^2 r$ where $r$ is the radius, and $\omega$    Further we know that $v=\omega*r$, therefore: $a_s=\frac{d}{dt}(\omega r)$  For constant acceleration $a_{total} = a_r + a_s = \omega ^2 r + \frac{d}{dt}(\omega r) =constant$  Further usefull information: Length of the track covered at a certain time $l=v*t=\omega r t$  With all this the radius will be a function of time, $r(t)$ and the angular velocity will be a function of time, $\omega (t)$  Boundary conditions: $r(0)  = 0$ $\omega (0) = 0$  Now I would like to find a possible set of solutions to create a track by implementing end boundary conditions that i choose e.g. $v(t_{end})=100 [m/s]$ and $l(t_{end})=5000 [m]$  Here is a diagram for clarity: How can I speed up D&D 3.5e combat? I'm looking for ways to speed up the combat in my D&amp;D 3.5 game. It seems that turns - both player and non-player - simply take too long. I have thought about giving everyone a 30 second timer, but I'm afraid that might inhibit their ability to come up with strategy and tactics. Living forever in D&D (via spells)? I was thinking of a way for a humanoid (PC or NPC) to live forever in a D&amp;D setting, but through rather "common" and reproducible means, such that they will be available to many. By this logic I exclude cases such as a god giving immortality (or some other intervention) or a unique item granting an endless lifespan etc.  To cover all bases I will note that miracle and wish cannot do this directly, nor can true resurrection (and its lesser brethren) "restore to life a creature who has died of old age".  I had came up with the following ruse:   Reach your deathbed with at least 2 HD (or levels). Have someone kill you so that the cause of death will not be "old age". Have a druid cast reincarnate on you into a young body. You "recall the majority of your former life". I assume your memories, personality/identity and experiences are preserved.   Rinse and repeat. It's not that difficult to recover the 1 HD lost through the course of almost a lifetime. The material components are worth 1,000 gp - might not be easy to get, but surely possible.  Furthermore, it is stated that "A wish or a miracle spell can restore a reincarnated character to his or her original form.". I assume the "original form" is the aged humanoid at his or her deathbed - not the direction we are looking for, unless it means that the humanoid restores his race only.  Is there a flaw in this plan? Is there another way of doing it? What does the "@" symbol do in SQL? I was browsing through the questions and noticed this:  SELECT prodid, issue FROM Sales  WHERE custid = @custid  AND datesold = SELECT MAX(datesold)               FROM Sales s               WHERE s.prodid = Sales.prodid                   AND s.issue = Sales.issue                   AND s.custid = @custid   I was wondering what the "@" does in front of custID?  Is it just a way of referencing the custID from the table being selected? There is a very bad problem with the "Blank screen" function in Ubuntu 17.10. I refer to the setting accessed via Settings->Power->Blank Screen. This seems to actually perform a screen lock, since I need to enter my password after un-blanking the screen. (However, given the behavior described below it's not clear exactly what this function actually does - maybe it just logs you out? maybe it reboots the machine?)  The problem is that a simple screen lock, which one would expect to lock the screen without affecting the state of any applications, in fact closes all applications that are open when the screen lock activates. In other words, if you have the screen lock set to 5 minutes, and you walk away from your machine to get a sandwich or whatever, when you come back and unlock the machine all your apps have closed without saving their state. So far, the only work-around I have found is to entirely disable screen locking in Ubuntu 17.10. My question is, how can this be fixed so that screen locking works properly - that is: the screen locks on schedule after a period of inactivity, and when unlocked all applications that were running are still running?  I am asking a new question for the following reasons:  1) The existing answers to (and comments on)  do not address the issue, and in fact misrepresent the actual problem in ways that make me think the comment writers have not understood what is happening;  2) I cannot usefully address that question because I do not have sufficient reputation to either upvote the question or comment on it, and I cannot answer the question because I have no idea why this problem occurs;  3) I will probably never achieve a reputation of 15, much less 50, on StackExchange. Which is fine, that's not among my life goals.  4) But this question is important and deserves to be addressed. It is a drastically unacceptable bug. How fast a (relatively) small black hole will consume the Earth? This question appeared quite a time ago and was inspired, of course, by all the fuss around "LHC will destroy the Earth".   Consider a small black hole, that is somehow got inside the Earth. Under "small" I mean small enough to not to destroy Earth instantaneously, but large enough to not to evaporate due to the . I need this because I want the black hole to "consume" the Earth. I think reasonable values for the mass would be $10^{15} - 10^{20}$ kilograms.   Also let us suppose that the black hole is at rest relative to the Earth.  The question is: How can one estimate the speed at which the matter would be consumed by the black hole in this circumstances? Update a field without changing the node I need to change a field in a node without altering the 'changed' timestamp. I know this was possible in Drupal 7 using field_attach_update(), but that has been removed since then.  I could use an update query and change the field directly in the database, but I was wondering if there is a better way (or a replacement for field_attach_update()).