Prove that there exists 5 consecutive numbers, each of which is divisible by a cube of a positive integer greater than 1.
Prove that for each $n$, there exist $n$ consecutive integers, each of which is divisible by a perfect square larger than $1$.
When should I publish in interdisciplinary versus subject-specific scientific journals? Show that the function $g(x) = x^2 \sin(\frac{1}{x}) ,(g(0) = 0)$ is everywhere differentiable and that $g′(0) = 0$ How can you sync Blender configs between multiple machines? How to scp in Python? Windows Update Slow on Vista Update I was able to get Readiness Tool to run but not the update Now the reediness tool will not even run Security Essentials will run    I have legal Windows 7 to install Do you think that is safe bet to try?    Had some performance issue so I ran MalwareBytes and Security Essentials.     It found some malware that was successfully removed.    I was able to Update Security Essentials and I ran it again for safety and it found nothing additions.     The last successful Windows Update was 5 days ago     Checking for Updates has been running 6 hours CPU 100%  network 0%     Windows6.0-KB947821-v35-x86.mnu fails to install It is supposed to be a tool to address update problems   I fear the registry got hacked to prevent updates     What can I do?  I know Vista.  I got it free. Using Image exportToDrive in Google Earth Engine? I want to export image to drive for my roi. For this i have specified a geometry(roi). But exported map doesn't cover the area specified and it's not showing the color palette. Is there any possible way to export a colored image (which shows in my layer) to Drive? Why it's not covering the region I have specified. Problem is in export.To.Drive section. But all the codes are given to check error that i did.  Code was:    var region = ee.FeatureCollection('users/karmakersourav/shape')   .filter(ee.Filter.eq('NAME_1', 'Chittagong'));   var addNDVI = function(image) {     var ndvi= image.normalizedDifference(['B4', 'B3']).rename('NDVI');     return image.addBands(ndvi);   };    var cloudMask = function(image) {     var clouds = ee.Algorithms.Landsat.simpleCloudScore(image).select(['cloud']);     return image.updateMask(clouds.lt(25));   };   // Select the land mask.   var landMask = function(image) {   var datamask = hansenImage.select('datamask');   // Create a binary mask.   var mask = datamask.eq(1);   return image.updateMask(mask);   };     // Load a Landsat collection, apply the NDVI and cloud/water masking functions over it.   var collection1 = ee.ImageCollection('LANDSAT/LE07/C01/T1_RT_TOA')     .filterBounds(region)     .filterDate('2008-01-01','2008-12-31')     .map(addNDVI)     .map(cloudMask)     .map(landMask)     .select('NDVI') ;   print(collection1);     //reducer   var annualNDVI = collection1.reduce(ee.Reducer.median());   var region_NDVI = annualNDVI.reduceRegions({     collection: region,     reducer: ee.Reducer.median(),     scale: 30 // the resolution of the dataset   });     var ndviParams = {min: -1, max: 1, palette: ['blue', 'white','green']};   var boundParams = {palette: ['black']};   Map.addLayer(annualNDVI.clip(region), ndviParams, 'NDVI', 1);    Map.addLayer(region, boundParams, 'LA', 1);    //here's the problem  Export.image.toDrive({    image: annualNDVI,    description: 'CTG_NDVi',    scale: 30,    region: roi,    fileFormat: 'GeoTIFF',    maxPixels: 1e12,    formatOptions: {       cloudOptimized: true     }   });     My imports was:  var image = ee.Image("UMD/hansen/global_forest_change_2015_v1_3"),       region = ee.FeatureCollection("users/karmakersourav/shape"),       hansenImage = ee.Image("UMD/hansen/global_forest_change_2015"),       roi = /* color: #98ff00 */ee.Geometry.Polygon(           [[[91.26571433292804, 22.382447200369512],           [91.70516745792804, 22.24015355729955],           [91.81503073917804, 21.50608889294255],           [91.99081198917804, 21.158146277513005],           [92.36434714542804, 20.74775339022756],           [92.38631980167804, 21.362918378188724],           [92.68868864595584, 21.285515736407884],           [92.66671598970584, 22.12251851402064],           [92.42501677095584, 22.964696114885136],           [92.43600309908084, 23.237540932485988],           [92.31515348970584, 23.620600408965007],           [92.21627653658084, 23.781555321668222],           [92.04049528658084, 23.691042604440895],           [91.90865934908084, 23.731278240693108],           [91.89767302095584, 23.47960242153599],           [91.75485075533084, 23.28800680321665],           [91.77682341158084, 23.08602889002461],           [91.61202848970584, 22.99503954262493],           [91.46920622408084, 23.277915158047364],           [91.34835661470584, 23.308187798303887],           [91.22750700533084, 23.600467103459394],           [91.28243864595584, 23.872005072934794],           [91.32638395845584, 24.082808607079368],           [91.24947966158084, 24.263221977268092],           [91.06271208345584, 24.223152164577193],           [90.73312223970584, 23.88205115062075],           [90.63424528658084, 23.660857737733508],           [90.54635466158084, 23.328365731356676],           [90.65621794283084, 22.83312931280329],           [90.98580778658084, 22.437667249990497],           [90.98580778658084, 22.071621721722586]]]); 10 hour layover in Moscow Russia, do I need a transit visa? On June 29th 2015, I will be traveling for the first time to Italy from USA. I will have a 10 hour layover in Moscow Russia. My question is, do I need a visa to visit the city? Padding trailing whitespaces in a string with another character I'd like to output hello world over 20 characters.  printf "%-20s :\n\n" 'hello world!!'  # Actual output hello world!!        :  # Wanted output hello world!!========:   However, I don't want to complete with spaces but with "=" instead. How do I do that? What is the format for e-mail headers that display a name rather than the e-mail? Polygamma function series: $\sum_{k=1}^{\infty }\left(\Psi^{(1)}(k)\right)^2$ Applying the , I found: $$S=\displaystyle\sum_{k=1}^{\infty }\left(\Psi^{(1)}(k)\right)^2\lt\dfrac{2}{3}\pi^2$$ where $\Psi^{(1)}(k)$ is the polygamma function. Is it known any sharper bound for the sum $S$? Thanks. Principled way of collapsing categorical variables with many levels? What techniques are available for collapsing (or pooling) many categories to a few, for the purpose of using them as an input (predictor) in a statistical model?    Consider a variable like  (discipline chosen by an undergraduate student). It is unordered and categorical, but it can potentially have dozens of distinct levels. Let's say I want to use major as a predictor in a regression model.  Using these levels as-is for modeling leads to all sorts of issues because there are just so many. A lot of statistical precision would be thrown away to use them, and the results are hard to interpret. We're rarely interested in specific majors -- we're much more likely to be interested in broad categories (subgroups) of majors. But it isn't always clear how to divide up the levels into such higher-level categories, or even how many higher-level categories to use.  For typical data I would be happy to use factor analysis, matrix factorization, or a discrete latent modeling technique. But majors are mutually exclusive categories, so I'm hesitant to exploit their covariance for anything.  Furthermore I don't care about the major categories on their own. I care about producing higher-level categories that are coherent with respect to my regression outcome. In the binary outcome case, that suggests to me something like linear discriminant analysis (LDA) to generate higher-level categories that maximize discriminative performance. But LDA is a limited technique and that feels like dirty data dredging to me. Moreover any continuous solution will be hard to interpret.  Meanwhile something based on covariances, like multiple correspondence analysis (MCA), seems suspect to me in this case because of the inherent dependence among mutually exclusive dummy variables -- they're better suited for studying multiple categorical variables, rather than multiple categories of the same variable.  edit: to be clear, this is about collapsing categories (not selecting them), and the categories are predictors or independent variables. In hindsight, this problem seems like an appropriate time to "regularize 'em all and let God sort 'em out". Glad to see this question is interesting to so many people! Please bring back the oldest sort order for answers, I think we can deal with four different types of sort order.  It's helpful if you don't want to have to tool-tip every post to see which got posted first, so that you can upvote the oldest answer when answers duplicate each other.  Edit:  Also, trying to read newest backwards doesn't work well for questions with multiple pages of answers. How can you enumerate an enum in C#?  E.g. the following code does not compile:  public enum Suit {     Spades,     Hearts,     Clubs,     Diamonds }  public void EnumerateAllSuitsDemoMethod() {     foreach (Suit suit in Suit)     {         DoSomething(suit);     } }   And it gives the following compile-time error:     'Suit' is a 'type' but is used like a 'variable'   It fails on the Suit keyword, the second one. What is mirror lockup and what is its primary function? My SLR is equipped with the mirror lockup function. What does it do, and when would I employ such a feature? I have been struggling for one hour with this simple problem (QGIS 1.8.0-Lisboa, Windows 7) :  I have a raster layer. I would like to display the label and not only the band value when I use the Identify Features button. Is it possible? What is the joint distribution of $Z=\min(X,Y)$ and $I_{Z=X}$? Assume that $X$ and $Y$ are independent random variables with $X \sim \exp(\lambda)$ and $Y \sim \exp(\mu)$. It is impossible to obtain direct observations of $X$ and $Y$. Instead, we observe the random variables $Z$ and $W$, where $Z = \min\{X,Y\}$ and $W =1$ if $Z=X$ and $W=0$ if $Z=Y$.  How to find the joint distribution of $Z$ and $W$? How can I execute `date` inside of a cron tab job? I want to create a log file for a cron script that has the current hour in the log file name. This is the command I tried to use:  0 * * * * echo hello &gt;&gt; ~/cron-logs/hourly/test`date "+%d"`.log   Unfortunately I get this message when that runs:  /bin/sh: -c: line 0: unexpected EOF while looking for matching ``' /bin/sh: -c: line 1: syntax error: unexpected end of file   I have tried escaping the date part in various ways, but without much luck. Is it possible to make this happen in-line in a crontab file or do I need to create a shell script to do this? $\epsilon$ undefined using Minion Pro with pdftex I'm using MiKTeX 2.9 and have recently installed the Minion Pro fonts for use with pdftex. I followed the instructions available on  to install them.  Everything works as expected, but in place of the Greek letter epsilon I get a box with a cross (see below), and the following warning:    I found the issue was reported , but I still can't fix it. xelatex works fine, but I'd like to to stick to pdftex so I can use microtype.  \documentclass{article}  \usepackage[T1]{fontenc} \usepackage{MinionPro}  \begin{document}  Text here. $\epsilon$  \end{document}       UPDATE: a set of instructions for the installation of the up-to-date FontPro scripts with MiKTeX can be found . JavaScript open in a new window, not tab enumitem breaks beamer's itemize despite fixes I thought I had tamed enumitem. I had this  and this .  Then I tried a [&lt;+-&gt;] construct. It failed. Commmenting the enumitem section prevents errors but I'd rather not have to do this.  On its current state, this code produces two errors, one because of the [&lt;+-&gt;] and another because of the \onslide.   \documentclass{beamer}   \usepackage{enumitem}  \setitemize{label=\usebeamerfont*{itemize item}%    \usebeamercolor[fg]{itemize item}    \usebeamertemplate{itemize item}}%https://tex.stackexchange.com/a/24491  \setenumerate[1]{%    label=\protect\usebeamerfont{enumerate item}%          \protect\usebeamercolor[fg]{enumerate item}%          \insertenumlabel.}%https://tex.stackexchange.com/a/45950   \begin{document}  \begin{frame}  \begin{itemize}[&lt;+-&gt;]  \item 1  \item 2  \end{itemize}  \onslide&lt;2&gt;{text}  \end{frame}  \end{document}