Hi guys can someone help me with this ?(Without using Modular arithmetic)  Show that if $p$ is a prime number $&gt;3$ then $24$ $\mid$ $p^2-1$
Let $p&gt;3$ be a prime. Prove that $24 \mid p^2-1$.   I know this is very basic and old hat to many, but I love this question and I am interested in seeing whether there are any proofs beyond the two I already know.
How can I resize (not compress) multiple images in a MS Word document? In a blank document, I insert images (screenshots - all are of same size and same format) from a folder. I want to resize the images to a desired size. All now I am doing is selecting one image by one, setting its size. Word does not seem to have multiselect working for images.  Ideally, I want to select multiple images set its size in one go with out use of a macro. How would I find the period of an oscillator with the following force equation?  $$F(x)=-cx^3$$  I've already found the potential energy equation by integrating over distance:  $$U(x)={cx^4 \over 4}.$$  Now I have to find a function for the period (in terms of $A$, the amplitude, $m$, and $c$), but I'm stuck on how to approach the problem. I can set up a differential equation:  $$m{d^2x(t) \over dt^2}=-cx^3,$$  $$d^2x(t)=-{cx^3 \over m}dt^2.$$  But I am not sure how to solve this. Wolfram Alpha gives a particularly nasty solution involving the hypergeometric function, so I don't think the solution involves differential equations. But I don't have any other leads.  How would I find the period $T$ of this oscillator? How to get the last value of an ArrayList How can I convert an std::string to a char* or a const char*? How to prove this sequent using natural deduction? How to import Illustrator swatch libraries into InDesign - Adobe Indesign Mac? I have a very reach swatch library in adobe-illustrator like food colors and.... But in adobe-indesign I don't have many colors. Why? Can I import them to indesign? SVM for unbalanced data I want to attempt to use Support Vector Machines (SVMs) on my dataset. Before I attempt the problem though, I was warned that SVMs dont perform well on extremely unbalanced data. In my case, I can have as much as 95-98% 0's and 2-5% 1's.   I tried to find resources which talked about using SVMs on sparse/unbalanced data, but all I could find was 'sparseSVMs' (which use a small amount of support vectors).  I was hoping someone could briefly explain:   How well SVM would be expected to do with such a dataset   Which, if any, modifications must be done to the SVM algorithm What resources/papers discuss this pkgloader is not finding l3regex I would like to try a package which seems interesting, but it some dependencies are not satisfied.   Here is my minimal example:  \documentclass{article}  \usepackage{pkgloader} \LoadPackagesNow  \begin{document}     pckloader trial \end{document}   And I get the following error: ! LaTeX Error: File 'l3regex.sty' not found.. Therefore, I tried to update my distribution with the linux commands  tlmgr update --self tlmgr update --all   But the package l3regex is still not foundable. Plus, my computer is not lying since l3regex.sty is not in my folder /texmf-dist/tex/latex/*.  So, is it something normal ? How can I workaround this problem ? I write about  that shows a big probability mass. It's a web-based interactive visualization of topics estimated using Latent Dirichlet Allocation that is built using a combination of R and D3; the default for scaling the set of inter-topic distances defaults to Principal Components, but other algorithms are also enabled.    This is the way that it finally shows with some data I found online and used to understand Latent Dirichlet Allocation topic modeling. As far as I understand, this graph is ideal to give out final names to each topic according to the frequency or relevance of each term given the topic but I've got two questions:   1. What would you simply say about topic 8 position on the graph? Meaning that I can't tell what each square represents in this graph, I can't tell in plain words what's the difference between topic 1 and 10, or topic 8 and 3, given their position on this graph?   2. What can you say about the big gray line in comparison with the red filling when lambda is 0? I think I get that when lambda is 1, it's meaning about plain frequency of the term in the whole corpus vs the frequency of the terms in that topic, but I'm not sure I get it with putting more weight in the ratio from red to gray: what is the gray line saying about that term and how is red contrasting?  You can get this for a model named lda_model$plot() found .   I am looking for the main idea at least. If there is info I need to add please tell me. How to change the font color of a disabled TextBox? Format timedelta to string Start modal operator from a click in panel I want to start a modal operator by clicking a button in a panel in the properties region. It should then stop when I click somewhere in the 3D viewport. I want to execute some code when I start and finish the operator (see the code below). I tried modifiyng the modal operator template with an execute method to start the modal operator. But the now the context.space_data.type is always &quot;PROPERTIES&quot; because that's where the panel is located, I guess. Is this a bad way of doing what I want? class MY_OPERATOR_OT_click_on_3dview(bpy.types.Operator):          bl_idname = &quot;mesh.click_on_3dview&quot;     bl_label = &quot;Click on 3D&quot;      def modal(self, context, event):                  if context.space_data.type != 'VIEW_3D':             return {'PASS_THROUGH'}                  if event.type in {'MIDDLEMOUSE', 'WHEELUPMOUSE', 'WHEELDOWNMOUSE'}:             # allow navigation             return {'PASS_THROUGH'}         elif event.type == 'LEFTMOUSE':             # DO ALL THE POST-SELECT STUFF             return {'FINISHED'}         elif event.type in {'RIGHTMOUSE', 'ESC'}:             return {'CANCELLED'}          return {'RUNNING_MODAL'}      def execute(self, context):         # DO ALL THE SETUP STUFF           context.window_manager.modal_handler_add(self)              return {'RUNNING_MODAL'}            def cancel(self, context):         print(&quot;CANCEL???&quot;) How can I remove the new weather information from the taskbar? A word for "every two days" Adding holes simultaneously within mesh Im trying to add multiple holes within my mesh, so I divided it up, and then used cylinders shapes to make the holes. On the top image I used the Boolean operation. And on the bottom image, I subdivided one of the rectangles and used the looptool method with the circle. Once I add a subdivision modifier I am getting weird result with the Boolean but the operation holes, but the bottom Hole looks more acceptable once cleaned up. Is one or the other method the correct way? Creating an index of quality from multiple variables to enable rank ordering I have four numeric variables. All of them are measures of soil quality. Higher the variable, higher the quality. The range for all of them is different:  Var1 from 1 to 10  Var2 from 1000 to 2000  Var3 from 150 to 300  Var4 from 0 to 5  I need to combine four variables into single soil quality score which will successfully rank order.  My idea is very simple. Standardize all four variables, sum them up and whatever you get is the score which should rank-order. Do you see any problem with applying this approach. Is there any other (better) approach that you would recommend?  Thanks  Edit:  Thanks guys. A lot of discussion went into "domain expertise"... Agriculture stuff... Whereas I expected more stats-talk. In terms of technique that I will be using... It will probably be simple z-score summation + logistic regression as an experiment. Because vast majority of samples has poor quality 90% I'm going to combine 3 quality categories into one and basically have binary problem (somequality vs no-quality). I kill two birds with one stone. I increase my sample in terms of event rate and I make a use of experts by getting them to clasify my samples. Expert classified samples will then be used to fit log-reg model to maximize level of concordance / discordance with the experts.... How does that sound to you? I have a spreadsheet full of addresses to geocode in ArcMap 10.  I've added the spreadsheet to the map, then started to geocode them via the context menu's "Geocode addresses" item.  Many were matched automatically, and most of the unmatched I've been able to resolve within the Interactive Rematch dialog. But I have a handful of addresses where I get no result at all.  I can, however, locate these points on Google Maps, and I can get the latitude and longitude that way.  How can I enter that data into the table to locate the missing points?  I have tried editing the data and putting the lat/lon values into the X and Y columns, (via Edit Features -> Start Editing, then Open Attribute Table on the context menu).  But when I Flash the point, I don't see it.  The lat &amp; lon are consistent with the other data points on the map (i.e., not swapped, and using the correct sign).  How can I add the points to the table? What are these cartridges that many characters have in the Star Wars movies? Admiral Ozzel has them on both sides of his uniform (upper chest).  Most Imperial officers seem to have them.  Han, pictured also here, has three such cartridges on his jacket.  I'd like to make such a jacket and use anything that looks like them.  I figure they are most closely related to cartridges for guns.  (which is what I imagine they are in the films).  But does anyone know the real scoop on them?  What is their purpose in the Star Wars universe?  Admiral Ozzel:    And Han Solo: Why is integration the inverse of differentiation, I mean why do I get the same function when I integrate and then differentiate the result? Can druids Wild Shape into creatures other than beasts? Under Wild Shape it says "assume the shape of a beast" you have seen before. Does this mean they can only transform into creatures that have the beast type, such as bear, wolf, crocodile, etc.? Or can they turn into things with other types, like dragon, monstrosity, humanoid, fiend, etc.?