SQL primary key, INT or GUID or..?
INT vs Unique-Identifier for ID field in database
Can sum of a rational number and its reciprocal be an integer?   My brother asked me this question and I was unable to answer it.   The only trivial solutions which I could think of are $1$ and $-1$.  As to what I tried, I am afraid not much. I have never tried to solve such a question, and if someone could point me in the right direction, maybe I could complete it on my own.  Please don't misunderstand my question.   I am looking for a rational number $r$ where $r + \frac{1}{r}$ is an integer. I write some choice questions into beamer frame, after some research, here is my code:  \documentclass[aspectratio=169]{beamer} \usetheme{Berkeley} \usepackage{tasks,CJK} \begin{document} \begin{CJK*}{utf8}{bsmi} \begin{frame} \transwipe 1.Which one you want to choose? \begin{tasks}[counter-format=tsk[A].,debug=true](4) \task A \task B \task C \task D \end{tasks} \end{frame} \end{CJK*} \end{document}   output with pdflatex:  But I don't want the D choice goto the second line, I want them stay in one line, what should I do? Series prove or disprove statement Let $a_n$ be a sequence. $\lim_{n\to\infty} a_n =0 $ then the series: $\sum_{n=1}^\infty a_n, \ \sum_{n=1}^\infty (a_n+a_{n+1}) $ converge and diverge together.  It doesn't seem right, there are no convergence tests that fit this question yet every counterexample I try does not seem to work. Is this how I should see the sum? $\sum_{n=1}^\infty (a_n+a_{n+1})=2\sum_{n=1}^\infty a_n +a_{n+1}$ If so then there's no real difference between the two series since you multiply it by a constant and add just one more value. Mandatory excerpt for custom post type Exporting QGIS project to Mapnik XML? Is it possible to export a QGIS project to Mapnik xml?   I'm using QGIS 2.4 and Quantumnik does not seem to work with that version. How to re-install http windows service I replaced apache webserver with http(WINHTTP windows service) for use virtual hosts feature. But I was missing  http(WINHTTP windows service) which I previously removed.I  now want to  reinstall this service for use print spooler. C's strtok() and read only string literals char *strtok(char *s1, const char *s2)      repeated calls to this function break string s1 into "tokens"--that is   the string is broken into substrings,   each terminating with a '\0', where   the '\0' replaces any characters   contained in string s2. The first call   uses the string to be tokenized as s1;   subsequent calls use NULL as the first   argument. A pointer to the beginning   of the current token is returned; NULL   is returned if there are no more   tokens.   Hi,   I have been trying to use strtok just now and found out that if I pass in a char* into s1, I get a segmentation fault. If I pass in a char[], strtok works fine.   Why is this?  I googled around and the reason seems to be something about how char* is read only and char[] is writeable. A more thorough explanation would be much appreciated. Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. How does the two slit experiment work? Whilst going through 'A brief history of time', I faced difficulty in understanding the . How can an individual electron cause fringes on screen? I was unable to understand it? Please explain it simply. Do the Imperials know they are evil? How to draw good arrows explaining parts of equation? It would be nice to allow users to mark a change in an answer (or question) as minor (e.g. for a simple spelling or grammar correction). A change marked as minor wouldn't push the question on top of the list of questions on the home page or in the feeds. It wouldn't trigger any notification. This could be implemented with a "Minor change" checkbox when editing an entry (a la Confluence). What do you think? How can I install a package without root access? I have no root access on this machine.  I would like to know if there is a way I can download Ubuntu packages and install them as non-root?  Probably in my ~/bin or ~/usr/share or something like that? Would that work? She don't know that she's a lucky girl Here's from an old song (1963) "" by Lesley Gore.       She don't know that she's a lucky girl   Here's another example, "Silence is Golden" (1964) by The Tremeloes [YouTube ]      Oh, don't it hurt deep inside to see someone do something to her.   I wonder how common it is to say "She don't" or "don't it". Do native English speakers often use these?  By the way, Lesley Gore is American, and the Tremeloes is British. Is there a way to set app-specific volume? How do I convert Word smart quotes and em dashes in a string? Can a hotel kick you out if you let an unregistered guest share a room with you? How can I run ssh-add automatically, without a password prompt? I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine?  I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine.  if [ -z "$SSH_AUTH_SOCK" ] ; then     eval `ssh-agent -s`     ssh-add fi I have a issue with my Drupal installation, for example:   when I enable or disable the modules, It redirects me to a blank page, when I create a new content type and save it, redirects me to a blank page, when I add a new view and save it, it redirects me to a blank page, when I try to clear the cache, it redirects me back to a blank page, or in similar cases.   Basically all the confirmation pages redirect me to a white screen. When I refresh it again, it shows me the page. I tried to increase the PHP memory value but it doesn't help.  Are there any other solutions for this?  The error which I'm having:      Fatal error: Allowed memory size of 100663296 bytes exhausted (tried to allocate 8192 bytes) in sites/all/modules/views/plugins/views_plugin_localization_none.inc on line 1 How Does The Debugging Option -g Change the Binary Executable? When writing C/C++ code, in order to debug the binary executable the debug option must be enabled on the compiler/linker.  In the case of GCC, the option is -g.  When the debug option is enabled, how does the affect the binary executable?  What additional data is stored in the file that allows the debugger function as it does?