If else statement involving two numbers in scientific notation
How to do integer & float calculations, in bash or other languages/frameworks?
"If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer" If $1/a  +  1/b  =  1 /c$   where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer.  I found this question in RMO 1992 paper !  Can anyone help me to prove this ?  May be it's too easy and simple . But , I'm just novice in number theory ! Tool for cleaning LaTeX code Is there something like indent for LaTeX? I have a collaborator that is using Scientific Workplace and the code it produces is totally messed up; I know I shouldn't expect miracles, but any machine support would be useful.  EDIT: This question is quite undefined without my comment to KeithB's answer; the idea is to save VC-friendly one sentence/one paragraph per text file line structure which SWT "fixes" by wrapping everything into fixed column width format. Short sci-fi story of plan devised by marooned spaceship pilot to save paradise world from development Spaceship crashes on beautiful, remote planet. The pilot survives and lives quite well on the beautiful "island paradise" world amongst friendly, good-natured people... but, one day (while relaxing in a hammock near a beach) he "realized he was dying" (actually, that he would eventually die, then being unable to help the people he had come to love). He fears future "discovery" of his adopted world and the inevitable plundering of the resources and people by "developers"... so he devises... "a plan" "convinced island elders to support his plan" "his students taught others" "achieved 80% literacy... a remarkable feat" "established world government" "more generous than developer expected" "successfully argued for independent status" "established 100% taxation rate" "finished resort buildings converted to school" "developer hired to build resort in isolated area"  ...'not having luck finding it... my recollection of the story is good, but apparently not EXACT/searchable phrases How do I troubleshoot a Windows freeze or slowness? A machine is described as being "really slow" or "freezing". How can I troubleshoot/resolve this issue? What should be the first steps to take? Is the CMB rest frame special? Where does it come from? It seems that we are . This is the speed of our galaxy relative to the cosmic microwave background. Where does this rest frame come from? Is this special in any way (i.e., an absolute frame)? EDIT: I think the more important question is &quot;where does the CMB rest frame come from?&quot;. How to replace plain URLs with links? I am using the function below to match URLs inside a given text and replace them for HTML links. The regular expression is working great, but currently I am only replacing the first match.  How I can replace all the URL? I guess I should be using the exec command, but I did not really figure how to do it.  function replaceURLWithHTMLLinks(text) {     var exp = /(\b(https?|ftp|file):\/\/[-A-Z0-9+&amp;@#\/%?=~_|!:,.;]*[-A-Z0-9+&amp;@#\/%=~_|])/i;     return text.replace(exp,"&lt;a href='$1'&gt;$1&lt;/a&gt;");  } ‘And what on earth’s a Squib?’ said Harry.   To his surprise, Ron stifled a snigger.   ‘Well – it’s not funny really – but as it’s Filch ...’ he said. ‘A Squib is someone who was born into a wizarding family but hasn’t got any magic powers. Kind of the opposite of Muggle-born wizards, but Squibs are quite unusual. If Filch’s trying to learn magic from a Kwikspell course, I reckon he must be a Squib. It would explain a lot. Like why he hates students so much.’ Ron gave a satisfied smile. ‘He’s bitter.’   Chamber of Secrets - pages 110-111 - British Hardcover   If a Squib is 'kind of the opposite of a Muggle-born wizards' wouldn't that make a Squib more Muggle than wizard? Does a Muggle strictly have to be born to Muggle parents to be considered a Muggle, or can the lack of magic render a person, even of wizarding parentage, a Muggle?  Hermione can say in all truthfulness that she is a 'Muggle-born witch.' The nickname (albeit derogatory) for a Muggle-born is 'Mudblood.' Filch can say in all truthfulness that he is a 'wizarding-born non-magic person,' which, according to Hagrid is a Muggle.  'Squib' may be derogatory in the same way as 'Mudblood' is. Neville laments his family thought he was a Squib when he showed no magical tendencies as a child; the Longbottoms were so rattled at the thought of Neville being a Squib that they, among other things, threw him out a second-story window to see if he would bounce. So could 'Squib' actually be a derogatory term meaning the opposite of 'Mudblood'? After all, the Ministry doesn't allow Squibs to register as magical beings, and many Squibs are schooled and trained in Muggle professions. Squibs don't get a Hogwarts letter.    Wizards can be born to Muggles. Can Muggles be born to wizards?  ETA 11.22.14: In regard to this question, I was glancing through Philosopher's Stone, and I came across this, that Neville said:     ‘Well, my gran brought me up and she’s a witch,’ said Neville, ‘but the family thought I was all Muggle for ages. My great-uncle Algie kept trying to catch me off my guard and force some magic out of me – he pushed me off the end of Blackpool pier once, I nearly drowned – but nothing happened until I was eight.’   Philosopher's Stone - page 93 - Bloomsbury - chapter seven, The Sorting Hat   Could what Neville says contribute to the theory and/or conclusion that Squibs are, or are not, Muggles? How do we apply what Neville said? Show that if a function is not negative and its integral is $0$ than the function is $0$ Suppose $f$ is continuous, $f(x) \ge 0$ on $[a,b]$ and $\int_a^b f(x) dx=0$. Show that $f(x)=0$ on $[a,b]$.   I know that if $f$ in continuous at $x_0$ and $f(x_0) &gt; 0$, then there exists $\delta &gt; 0$ s.t. $f(x) \ge \frac{1}{2} f(x_0)$ for $|x-x_0| &lt; \delta$ and I think it should help me but I'm stuck at this point. Lately my laptop (HP g42 247sb) screen is damaged, so I hook it up with an external monitor (LG something) and it works fine now.  The only annoying thing is I cannot navigate the BIOS menu for some tweaking because the BIOS not shown on the external monitor, instead, it only shown on the broken laptop screen, and  it only output to my external monitor when Windows/OS is logged-on.  So, is there anyway I can force output during BIOS/BOOT/POST to my external monitor?  Things I have done and didn't work:   Set my LG monitor as primary display on both window properties and Intel Graphics panel  Enter the BIOS (F10 key) and press the Fn+F4 key (change display output). Disable and uninstall my internal screen (broken laptop screen) using device manager and restart, but Windows (BIOS?) install it back on log-on. Closed lid/Magnet on sensor. Conjugate class in the dihedral group Cardinalities of the intervals $(-1,1)$ and $[-1,1]$ How to tell the probability of failure if there were no failures? I was wondering if there is a way to tell the probability of something failing (a product) if we have 100,000 products in the field for 1 year and with no failures? What is the probability that one of the next 10,000 products sold fail? Does a (half) beheaded Ettin take bleeding damage of some sort? Let's say a character cuts off one of an Ettin's heads, but the other head is still intact, and it's as such still alive. Obviously, there's a lot of blood. Does the Ettin take continuous damage from naturally bleeding out? Or does it not work that way? Write Python stdout to file immediately When trying to write the stdout from a Python script to a text file (python script.py &gt; log), the text file is created when the command is started, but the actual content isn't written until the Python script finishes. For example:  script.py:  import time for i in range(10):     print('bla')     time.sleep(5)   prints to stdout every 5 seconds when called with python script.py, but when I call python script.py &gt; log, the size of the log file stays zero until the script finishes. Is it possible to directly write to the log file, such that you can follow the progress of the script (e.g. using tail)?   EDIT It turns out that python -u script.py does the trick, I didn't know about the buffering of stdout. When I visit a website it sometimes puts cookies on my browser. Usually cookies keep track of browsing info from that particular site. If I don't delete those cookies and browse other websites, will the cookies be able to know which site I am browsing? Also, can any website read browsing history which is saved by browsers? Can any website know about my browsing history by help of cookies, browsing histories saved by browsers, or by any scripting language e.g. javascript? Here's my code:  x = 1.0 y = 100000.0     print x/y   My quotient displays as 1.00000e-05.  Is there any way to suppress scientific notation and make it display as 0.00001? I'm going to use the result as a string. Cardinality of a set A is strictly less than the cardinality of the power set of A How to get the list of properties of a class? How to reduce memory usage on a Unix webserver I'm currently using a Joyent Accelerator to host my webapps, and it's working fine, however I need to reduce costs so I'm downgrading my current plan and that imposes some new memory limits (256M rss, 512M swap). I wasn't too far over them yesterday, but after restarting Apache several times today, I'm now 411M rss, 721M swap (prstat -Z -s cpu).  Searching in Server Fault only gives me lots of ways and specific tools to monitor the server, but no advice on how to reduce/optimize it's memory usage. I've also seen , but I don't think it's good for this particular (or may I say generic?) situation.  The server is running Solaris on a shared CPU, and I'm using a Apache + MySQL + PHP stack.  I'm interested in knowing the steps one can take to troubleshot this and solve the issues. However, I'm also running out of time to lower my memory foot print and downgrade the plan before the current ends, so anything that can make magic and save the day is welcome as well :) Using a naked black hole as a mirror? The YouTube video is a good example how the gravity of this merging binary black holes bend light around themselves.