Show that for any integer not divisible by 2 or 5, there is a multiple of it which is a string of 1s.
Primes dividing $11, 111, 1111, ...$
Is there any way to set a system wide memory limit a process can use in Windows XP? I have a couple of unstable apps which do work ok for most of the time but can hit a bug which results in eating whole memory in a matter of seconds (or at least I suppose that's it). This results in a hard reset as Windows becomes totally unresponsive and I lose my work.  I would like to be able to do something like the /etc/limits on Linux - setting M90, for instance (to set 90% max memory for a single user to allocate). So the system gets the remaining 10% no matter what. What are the differences between Factor Analysis and Principal Component Analysis? Polygon label repeated for each tile Is there a reason why the pin diagram of an RJ-45 looks like this?    I understand that the orange pair is used for Tx and the green pair for Rx. Why is it that the orange pair are kept together while the green pair are separated?  What are the consequences of messing around with this order as long as it is the same at both the ends? Removing extra page before and after \tableofcontents My main file generate extra page before \tableofcontents with header title "Table of contents". How can I remove this page?  I am copying the main.tex file code for your reference.   \documentclass[twoside,12pt]{Classes/aesm_edspia}  \begin{document} \addtocounter{page}{-1} \makethese  \onehalfspacing \newpage\thispagestyle{empty}\addtocounter{page}{-5}   %depth in the table of contents and section numbering \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \frontmatter  \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Acknowledgements} \fancyfoot[RO]{\thepage} \fancyfoot[LE]{\thepage} \renewcommand{\headrulewidth}{0.5pt} \renewcommand{\footrulewidth}{0pt}  \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Table of Contents} \fancyfoot[RO]{\thepage} \fancyfoot[LE]{\thepage} \renewcommand{\headrulewidth}{0.5pt} \renewcommand{\footrulewidth}{0pt}  \input{Abstract/Abstract}  \tableofcontents \listoffigures \listoftables   \mainmatter \pagestyle{fancy} \fancyhf{} \fancyhead[LE,RO]{Introduction} \fancyfoot[RO]{\thepage} \fancyfoot[LE]{\thepage} \renewcommand{\headrulewidth}{0.5pt} \renewcommand{\footrulewidth}{0pt}   \end{document} There is a lemma that says if a group $G$ has no proper nontrivial subgroups, then $G$ is cyclic. And here is the proof of the lemma:     Suppose $G$ has no proper nontrivial subgroups. Take an element $a$ in $G$ for which $a$ is not  equal to $e$. Consider the cyclic subgroup $\langle a \rangle$. This subgroup contains at least $e$ and $a$, so it is not trivial. But $G$ has no proper subgroups, so it must be that $\langle a \rangle = G$. Thus $G$ is cyclic, by definition of a cyclic group.   But here i do not understand the following: Why must $\langle a \rangle$ be a subgroup of $G$? For every single element $a$ in $G$, if $\langle a \rangle$ is a subgroup of $G$, then every group should have at least as many subgroups as the number of its elements. I would appreciate any help. Thanks Why does the /winsxs folder grow so large, and can it be made smaller? A Vista virtual machine I use only has a 10 GB virtual hard disk -- and I'm worried about it running out of space over time. I used  to check for the culprits..  And the primary culprit is that /winsxs or &quot;Windows Side-By-Side&quot; folder.  What is the Windows Side By Side folder? Well, that's .  All of the components in the operating system are found in the WinSxS folder – in fact we call this location the component store.  Each component has a unique name that includes the version, language, and processor architecture that it was built for.  The WinSxS folder is the only location that the component is found on the system, all other instances of the files that you see on the system are “projected” by hard linking from the component store.  Let me repeat that last point – there is only one instance (or full data copy) of each version of each file in the OS, and that instance is located in the WinSxS folder.   So looked at from that perspective, the WinSxS folder is really the entirety of the whole OS, referred to as a &quot;flat&quot; in down-level operating systems.  This also accounts for why you will no longer be prompted for media when running operations such as System File Checker (SFC), or when installing additional features and roles. That explains why the folder starts off big, but not why it gets larger over time – the answer to that question is servicing.   In previous versions of Windows the atomic unit of servicing was the file, in Windows Vista it’s the component.  When we update a particular binary we release a new version of the whole component, and that new version is stored alongside the original one in the component store.  The higher version of the component is projected onto the system, but the older version in the store isn’t touched.  The reason for that is the third part of why the component store gets so large.  Lots of other people :  A coworker recently received his every two year work laptop refresh and was in the middle of loading his new laptop with Vista. For some reason, his hard drive C: was partitioned to only 25GB and the rest of the space reserved for a much larger drive D:. Anyway, after loading many Windows Updates, he was left with hardly any drive space left on C:, and for some reason, the WinSxS directory had ballooned to over 8GB. While I knew what the WinSxS (Windows Side-by-Side) directory was for, I wasn't quite sure why that directory would explode in size so fast with normal operating system updates.  I don't really care about having all these duplicate files for safety, but I do care about the VM exploding due to an out of disk space error. So.. can /winsxs be safely pared down in any way? ..  Administrators should not, for any reason, take it upon themselves to clean out the /winsxs directory - doing so may prevent Windows Update and MSI from functioning properly afterwards.  Preventing accidental deletion from the directory is accomplished by putting a strong security descriptor on the directory that inherits to its children.  If this /winsxs folder gets any larger, I'm going to have to re-image this virtual machine.. which I really don't want to do! Can I have multiple background images using CSS? Is it possible to have two background images?  For instance, I'd like to have one image repeat across the top (repeat-x), and another repeat across the entire page (repeat), where the one across the entire page is behind the one which repeats across the top.  I've found that I can achieve the desired effect for two background images by setting the background of html and body:  html {     background: url(images/bg.png); }  body {     background: url(images/bgtop.png) repeat-x; }   Is this "good" CSS?  Is there a better method?  And what if I wanted three or more background images? How to find out client ID of component for ajax update/render? Cannot find component with expression "foo" referenced from "bar" Jumping in an elevator? If you search for something on "all sites" (using the searchbox at the top of , you'll reach the search results, e.g.  .  If you click directly on a tag on that page, e.g.        You get 404 Page Not Found error, e.g.     Steps to reproduce   Go to  and enter e.g. "keyforge" into the "Search all sites" field. Arrive at  Click on the "keyforge" tag below a search entry. Reach  (404 page not found)   Expected behaviour  Reach   System Info  Happens in both Firefox and Vivaldi browsers on Windows 10. What can I use to typeset MATLAB code in my document? This question led to a new package:      Does anybody have a quick and easy way to typeset some relatively long MATLAB code in the appendix? I looked up a few methods, and the mcode package emerged as a possibility, but it seems to be unmaintained...  I have a ton of equations in my code, so I'd prefer a solution that avoids having to use $ to denote equations.  Also, if possible, if there's a way to keep all of MATLAB's "natural" coding colors (e.g. green for comments), that would be great...  Any idea? How do high traffic sites service more than 65535 TCP connections? Why do my lamps require an insane "strength" value of 1 million? recently, I was using mesh planes to emit some light, and they had a strength of 8.0.. this worked well now, I want to swap these out for area lamps (to improve performance) i've positioned these area lamps in the place of my emitter polygons i've scaled them such they have 1.0 transform scale, and in the lamp settings, I set the size to 1m across (to size-match the previous emitters) the problem is, the lamps require a crazy "strength" of at least 1 000 000 (one million!) to produce any reasonable amount of light... this seems bonkers! point lamps, area lamps, and the others, are all effected my scene is scaled using the Centimeters preset.. the foreground is only a meter a way, and the more distant background is more like 5 meters back i've paid special attention to the sizing and scaling of this scene, I can't figure out why the mesh emitters are working with a sane Strength of 8, and the lamps require something out of this world? something must not be right...     Edit: Remastered scene corrects scales, problem persists       i've remastered the scene so that all of the objects have a proper scale factor of 1.0 this should correct any sizing discrepancy/confusion my scene must be in centimeters preset, all my other work is in centimeters the area lamp size is now definitely 1m, as highlighted in the above screenshot (and it is not affected by the 1.0 transform scaling factor, also highlighted (I also verified the delta scale is also 1.0)) despite correcting the scaling of my scene, strength 1 000 000 is still required is blender simply not accounting for my scene's Unit Scale setting? How to find application's path from command line? For example, I have git installed on my system. But I don't remember where I installed it, so which command is fit to find this out? Can moving tables to another MySQL database help performance? I want to know if I using different databases can help performance.  I have one big table support_chat with more than 5 million rows. I need to scan this all the time (3s with ajax) to check new messages on support.  If I move this table to another database in the same computer, can it help anything? (let users, sells, comments table faster)  For example:  db1  users table sells table comments table support_chat table // move this table to db2   db2  support_chat table   They want to keep old things due legal reasons, to have a user support history. How do candles and wicks work? Why was this very low quality flag declined? Question (since closed and deleted): . I know about the  of VLQ flags, and I can't fathom why anyone would think that question wouldn't be a candidate for removal.  Question text, for posterity:     Hey I want a Cyrus beck line algorithm program in c or c++. I have   searched a lot but hadn't got anything over Web..!!      If anyone of you have Program please give it to me and help me out.      Thank you in advance :)   I find  not compelling because it requires me to accept the premise that this question was not "unlikely to be salvageable". Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$? Whenever $X$ is a topological space, let us say that continuity on $X$ is detected by $\mathbb{R}$ iff for all functions $f : X \rightarrow Y$ where $Y$ is another topological space, we have that if every continuous function $c : \mathbb{R} \rightarrow X$ satisfies "$f \circ c$ is continuous", then $f$ is itself continuous.   Clearly, continuity on $\mathbb{R}$ is detected by $\mathbb{R}$ It is shown  that continuity on $\mathbb{R}^2$ is detected by $\mathbb{R}$. Clearly, it is not the case that continuity on $\mathbb{Q}$ is detected by $\mathbb{R}$, since every continuous mapping $\mathbb{R} \rightarrow \mathbb{Q}$ is constant.      Question. Do there exist general conditions underwhich we can conclude that continuity on a topological space is detected by $\mathbb{R}$? I have to determine how many six-integer subsets of $\{1, 2, 3, \ldots, 20\}$ are possible if no two consecutive integers are in a set.