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Cube of an integer $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=k$ and $x, y, z, k$ are integers.  Prove that $xyz$ is cube of some integer number.    I was wondering about giving a parametrization for the rational points on the elliptic curve in $\mathbb{P}^2(\mathbb{R})$ $$ x^2 y + y^2 z + z^2 x = k xyz$$ but I am not too confident in the topic, so I am asking you to shed some light.  Thank you for your help. PCB opaque coating for anti reverse engineering? Im trying to find a coating for my PCB in order to protect it from reverse engineering. I want it opaque, non-conductive and with a low thermal resistance.  Basically I do not want that someone replicates my circuit easily. I´ve beens searching a lot on coatings but did't find anything that suits to all my requirement. Anyone with an idea? I've got a directory shared on my network, using Samba. People on the netwerk use this Samba share to download files from my share to their computers. I'm interested in what files are downloaded most, and by which users they are downloaded. I'd like to see this in real time, if possible. Is there a program that allows me to do this? If yes, how can I use it?    I'm using Ubuntu 11.10. Consider a common proof of the uncountability of $(0,1]$, as presented  for example:  We assume that the reals can be arranged in a sequence $x_k$, represent every number in $x_k$ by its nonterminating decimal expansion, use the diagonal argument to create a sequence of decimal digits that differs from the nonterminating decimal expansion of each number in $x_k$ and then claim that this sequence of digits so generated must be the decimal expansion of some number not in $x_k$.  My problem is with this last step. Could it not be the case that the new sequence of digits is just the terminating decimal expansion of some number already in $x_k$?  Would it not be more correct to use the sequence $x_k$ to generate a sequence of all (both terminating and non-terminating) decimal expansion of all numbers in $[0,1)$ and then apply the diagonal argument? "Require Installation Of Untrusted Packages" while upgrading with the update manager It didn't fixed the error. So, how do I fix my GUI update?  For every software I have to install it from command line because I got same error when install software from Ubuntu Software Center. How do I remap a key in macOS Sierra, e.g., Right Alt to Right Control? I have rigged up a notch filter from . See below: -     Its the first circuit. Now I am trying to calculate its transfer function. I have calculated two equations, but I need the third one:   (Vin-V2)/(1/SC1) = V2/R3 (Vin-V1)/R1 = (V1-Vo)/(R2+(1/SC2))   V1 and V2 are the potentials at the input of the op-Amp. Standard error of a ratio I have a linear regression and two estimates, say A and B and their standard errors. I need to find the standard error of a ratio A/B [or A/(1-B)].  I guess the main problem is that I don't know the correlation between A and B. I also guess that makes this unsolvable, since the correlation plays a major role. Is this correct?  If I knew it, what would be the way to calculate the standard error? filling an occluded plane with the smallest number of rectangles I've got a specific problem which I'll try to describe as clearly as possible.   I have a defined rectangular region on a cartesian plane, and within that region there are other given rectangular sub-regions that are described in terms of their 4 vertices, ie {(x1, y1), (x1, y2), (x2, y1), (x2, y2)}, so that these regions form 'occlusions' on the plane. These regions don't overlap, but they can form more complex polygons when different-sized rectangles adjacent to each other appear joined.  here's an illustration:   I am interested in the space between these shapes, and how to define the space in the same way the occlusions are defined, that is as a set of rectangles. In particular I want the definition optimised so that the space is described using the smallest possible number of rectangles. For example, an incomplete rendering might look like this:   Can anyone suggest a way forward with this? How can I have the original set of vertices (describing the black rectangles) generate the 'complementary' set of vertices (red rectangles) such that the number of red rectangles is minimal?  I suspect it's a variation of a 'packing problem', but I have a feeling it might be fairly simple... Why there is no operator for time in QM? Applying graduated renderer in PyQGIS? Just trying to run the following code already given in the pyqgis cookbook to create graduated colors symbology (as in example with 2 classes)  I define the source info for the shapefile but when I run execute the code within my test-plugin, it just adds the layer without classifiying. Just adds as usual, all polylines appear same.  Any solution or working code/method?  link to code in cookbook   from qgis.core import  (QgsVectorLayer, QgsMapLayerRegistry, QgsGraduatedSymbolRendererV2, QgsSymbolV2,QgsRendererRangeV2)  myVectorLayer = QgsVectorLayer('C:/my_test_shape_file.shp', 'test_shp_file', 'ogr')  myTargetField = 'target_field' myRangeList = [] myOpacity = 1  # Make our first symbol and range... myMin = 0.0 myMax = 50.0 myLabel = 'Group 1' myColour = QtGui.QColor('#ffee00') mySymbol1 = QgsSymbolV2.defaultSymbol(myVectorLayer.geometryType()) mySymbol1.setColor(myColour) mySymbol1.setAlpha(myOpacity) myRange1 = QgsRendererRangeV2(myMin, myMax, mySymbol1, myLabel) myRangeList.append(myRange1)  #now make another symbol and range... myMin = 50.1 myMax = 100 myLabel = 'Group 2' myColour = QtGui.QColor('#00eeff') mySymbol2 = QgsSymbolV2.defaultSymbol(myVectorLayer.geometryType()) mySymbol2.setColor(myColour) mySymbol2.setAlpha(myOpacity) myRange2 = QgsRendererRangeV2( myMin, myMax, mySymbol2, myLabel) myRangeList.append(myRange2)  myRenderer = QgsGraduatedSymbolRendererV2('', myRangeList) myRenderer.setMode(QgsGraduatedSymbolRendererV2.EqualInterval) myRenderer.setClassAttribute(myTargetField) myVectorLayer.setRendererV2(myRenderer) QgsMapLayerRegistry.instance().addMapLayer(myVectorLayer)      @Kelly's code works perfectly.   However I noticed that both the code (one I have typed in my first message and yours in the 2nd message) DO NOT work in QGIS v1.7.3 but WORKS in QGIS v1.8.0. I think this was a bug(?) that already resolved in v1.8.0  And one more question;  Do you have any sample code for (natural breaks, Jenks) classification of the "numeric_attribute_field" based on given number of classes (i.e. no of classes will be a variable in the code, say "n", and I will pass that from the plugin GUI i.e. n = spinBox.value() ) I have an iPhone 5 running iOS 9.1 and a Macbook Pro running Yosemite.  Both devices are set up to sync photos to and from iCloud.  When I take a photo on the iPhone (for further processing on the Macbook), it takes an inordinate amount of time until the photo shows up in the Macbook's photos library - sometimes up to 10-20 minutes. Sometimes it seems to work faster if I quit the Photos app on both devices, and start it again.  I often end up sending myself photos through E-Mail because it's quicker. That seems ridiculous!  Is there a way to force a sync on the iPhone, or to speed up the process some other way? How to make clickable links and cross-references in pdfs produced by LaTeX? PuTTY inserts random characters during a session I recently started renting space on a remote server so that I could work on a project. I found that a relatively painless way to access it on a windows machine is through PuTTY. However, there is one thing that has always irked me when using it: for seemingly no reason random characters are sometimes inserted at the cursor.  Most of the time it is just a single tilde, but rarely it spits out what looks like some escape sequence ([[^8 or the like). It will only occur when I am focused on the window, whether I am typing or 20 feet away from the keyboard. If left for long enough, it will spit tildes at random intervals (average is about 1 minute).  Finally, this behavior seems to be inconsistant when running programs such as nano or the mysql interface: in nano, instead of inserting tildes, it will set marks (ctrl-^); in mysql, lines will become un-editable.  My question is this: Has anyone else experienced this sort of behavior in PuTTY? And if so, what can be done to prevent/correct this behavior? Are the endings "-zation" and "-sation" interchangeable? What is with words that have forms that end both in -zation and -sation, such as localization and localisation?  Many spell checkers recommend -zation. Ubuntu in VirtualBox wants to install on every boot OAuth 2.0 access token request failed with error "must use HTTP POST" OAuth 2.0 Auth token request failed with below error   { "error": "invalid_request", "error_description": "must use HTTP POST" }   What does this error mean?  I am using Postman. Have a connected app. I have used Post method, Url has https. Same request works for other Orgs. Did I missed any configuration/Permission check?  https://testOrg.lightning.force.com/services/oauth2/token?grant_type=password&amp;client_id={{CLIENT_ID}}&amp;client_secret={{CLIENT_SECRET}}&amp;username={{USER_ID}}&amp;password={{PASSWORD}} Error: 'else' without 'if' What are the system requirements for each flavour of Ubuntu Desktop? Why does the "Unanswered Questions" tab show questions that have answers? Why does the "Unanswered Questions" tab show questions that have answers?