Find gcd(15570555, 10872579)
How do I prove that 15462227 and 15462229 relatively prime?
I am making a fudge recipe that calls for 1cup whole milk and 5 cups sugar. It also uses 2 sticks of butter and 25 marshmallows. I'm wondering if I can omit the milk and cut back on the sugar by using sweetened condensed milk. How does the twitter bot work? How to rig a shirt with buttons so that the buttons follow the mesh of the shirt I didn't address this in a while because I was busy with something else, but now it has cycled back into my schedule.  Right now I have a shirt modeled and bones set in place. It's already technically rigged, but the only issue is the buttons.   I'm not entirely sure how to go about connecting them to the shirt's deformations. I tried to combine them and the shirt into one object, but because of the shirt's modifiers, (Solidify and subsurf, which I don't want to apply yet), the buttons become extremely deformed. I've tried to match the weight painting intensity where a button is at in correspondence with the shirt, but that doesn't seem to work, maybe it has to do with the specifics of where the button is?   Is there a way to make the buttons follow the shirt's deformations without deforming the mesh vertices of the button? I know that if I probably apply the modifiers on the shirt and combine it with the buttons, it would be okay, but I'm not okay with doing that just yet with the shirt.    I rigged the shirt by deleting all vertex groups, assigning empty groups to the mesh from the armature, and then assigned automatic groups in the weight paint menu.  Is there a way to do this? Problems with booting the system I have yesterday updated packages and today the system cannot boot properly. After seeing the Kubuntu logo there is a black screen which shows repeatedly.     Stopped User Manager for UID 121.      Removed slice User Slice of gdm.      Created slice User Slice of gdm.       Starting User Manager for UID 121...      Started Session c3 of user gdm.       Started User Manager for UID 121.   Please see the screenshot below An infinite subset of a countable set is countable In my book, it proves that an infinite subset of a coutnable set is countable. But not all the details are filled in, and I've tried to fill in all the details below. Could someone tell me if what I wrote below is valid?  Let $S$ be an infinite subset of a countable set $T$. Since $T$ is countable, there exists a bijection $f: \mathbb{N} \rightarrow T$. And $S \subseteq T = \{ f(n) \ | \ n \in \mathbb{N} \}$. Let $n_{1}$ be the smallest positive integer such that $f(n_{1}) \in S$. And continue where $n_{k}$ is the smallest positive integer greater than $n_{k-1}$ such that $f(n_{k}) \in S$. And because $S$ is infinite, we continue forever. Now consider the function $\beta : \mathbb{N} \rightarrow S$ which sends $k \rightarrow f(n_{k})$.   So in order for $S$ to be countable, $\beta$ would have to be a bijection. $\beta$ is injective since if $f(n_{k}) = f(n_{j})$, then $n_{k} = n_{j}$ because $f$ is injective. We also can conclude $k = j$ because the various $n_{i}$ chosen were strictly increasing.   Edit: $\beta$ also needs to be surjective. So for every $r \in S$ there exists a $q \in \mathbb{N}$ such that $\beta(q) = f(n_{q}) = r$. We know that $f^{-1}(r) \in \{n_{1}, n_{2}, ..., n_{k} ... \}$, so we can let $f^{-1}(r) = n_{d}$. Thus $\beta(d) = f(n_{d}) = r$. Deriving a QM expectation value for a square of momentum $\langle p^2 \rangle$ I already derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle=  \int\limits_{-\infty}^{\infty} \overline{\Psi}  \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And I can read clearly that operator for momentum equals $\widehat{p}=- i\hbar\frac{d}{dx}$. Is there an easy way to derive an expectation value for $\langle p^2 \rangle$ and its QM operator $\widehat{p^2}$? How to count the node a user has created in a View? In Python, I can compile a regular expression to be case-insensitive using re.compile:  &gt;&gt;&gt; s = 'TeSt' &gt;&gt;&gt; casesensitive = re.compile('test') &gt;&gt;&gt; ignorecase = re.compile('test', re.IGNORECASE) &gt;&gt;&gt;  &gt;&gt;&gt; print casesensitive.match(s) None &gt;&gt;&gt; print ignorecase.match(s) &lt;_sre.SRE_Match object at 0x02F0B608&gt;   Is there a way to do the same, but without using re.compile. I can't find anything like Perl's i suffix (e.g. m/test/i) in the documentation. How do I allow non-root access to /ttyUSB0? Since I updated from Ubuntu 10.04 (Lucid Lynx) to Ubuntu 12.04 (Precise Pangolin), I am unable to access the device connected in /ttyUSB0 if I don't have root access.  To be more specific, I use a USB-to-serial com port converter to access and configure Cisco equipment with software called . It happens that, since I upgraded to 12.04, PuTTY only sees the connected device when I run it as gksudo putty. If not, it says "unable to connect to port /ttyUSB0".  I have managed to change the permissions via chmod 666, and it works, but if I disconnect the USB device and reconnect, it goes back to root only. How do I permanently allow non-root access? I have a clue it might be via  rules, but I have no idea how to do it.  Obs.: Manufacturer and drivers are "PROLIFIC" I have a 3-wire  that looks like this:    I'm trying to wire it up to my Arduino to detect changes in weight. From what I understand, the changes in voltage are so small that the Arduino can't detect the changes without amplifying the voltage. So I bought an  at  that looks something this:    I found  that shows how to wire everything up. However, I can't figure out the schematic and why they are using two load sensors instead of just one. They also mention resistors but I'm not sure why they are using them (and why the sizes they chose), or where in the circuit to put them.  Can someone please help me figure out how to wire this thing up to detect changes in voltage? Also, is there a way to do this by using only one of these sensors? This is what I've done so far:    The amp also has some pins that I don't understand: Offset null, NC. What are these pins for? Should I be using them?  Update: Now I am working with an Instrumentation Amplifier (). I also now have a 4-wire load sensor that I am playing with. Still can't get it to work, but I thought I would try to understand that before moving to the 3-wire load sensor. Note: The legacy Skype for Linux application (v4.*) is now discontinued and was removed from Canonical’s partner repositories, so this question and its answers are obsolete. Please refer to  of our .    I am receiving the following message while I am trying to install Skype:  nidhin@ubuntu:~$ sudo apt-get update nidhin@ubuntu:~$ sudo apt-get install skype Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  skype : Depends: skype-bin but it is not installable E: Unable to correct problems, you have held broken packages   How can I fix this? Cannot select vertices from different object while in edit mode Whenever I enter edit mode, with 2 separate meshes (cubes), I can only select vertices/edges/faces of 1 mesh.  Example (the screen shot did not include the mouse cursor):    Also, when I enter edit mode with both meshes selected, one of the meshes has a red border and cannot be selected (it also has this border in Object mode): Is it possible to delete multiple elements from a list at the same time? If I want to delete elements at index 0 and 2, and try something like del somelist[0], followed by del somelist[2], the second statement will actually delete somelist[3].  I suppose I could always delete the higher numbered elements first but I'm hoping there is a better way. Is there a closed form expression for $1 + x + x^{4} + x^{9}+x^{16}+x^{25} +..+x^{k^2}$? We all know what the sum of a geometric series is  $1 + x + x^2 + x^3 + ... + x^k = \frac{x^{k+1} - 1}{x - 1}$ .  I was wondering if similar formulas exist in case the exponents  form some other sequence, for example are squares or cubes of positive integers? How much web can Spider-Man produce? Especially if he is not using his  but .   Also what happens to the web that he leaves behind? Does it decay after certain time or lose it stickiness and drops off? What is the equation for the tension on the ends of a cable suspended at different heights? I'm looking for an equation to find the tension on the ends of a cable suspended between two poles (one higher than the other) with no load but the cable itself.    I determined that the tension would be different on each end, that the shape of the suspended cable would be a  truncated at one end, and that the following would be the variables necessary in the equation:   cable weight cable length vertical distance between ends horizontal distance between ends   Some links that could be helpful: Combining randomForests in R, why are the err.rate, mse and rsq components NULL From ?combine in :     The confusion, err.rate, mse and rsq components (as well as the   corresponding components in the test compnent, if exist) of the   combined object will be NULL.   Why are the err.rate, mse and rsq components for the combined NULL? Is there an efficient way to re-calculate these metrics?  I ask because I would like to figure out a way to use the oob re-sampling method with the parRF model in . I've downloaded the new iOS 8 update on my iPhone 5 but am getting second thoughts about actually installing it.  Is there a way for me to delete that download or am I at the point of no return? 100% confidence interval for mean Is it possible to apply the law of the iterated logarithm (e.g. ) to derive non-trivial (i.e. bounded) 100% confidence intervals for population averages?  An abstract () gives at least such hint. However, its first reference by Robbins () does not seem to cover such result, as pointed out in @whuber's comment.  Edit: After justified comments by @whuber, I reformulated the question. General trigger bulkification - best practices A general question asked from time to time on stack exchange is question of trigger bulkification.  Therefore I have 2 questions:   Which best practices are you using? What is the best way to handle updates of more than 200 records? (In case of more than 200 records the trigger is executed more than once.)