$gcd(a,b)=lcm(a,b)$ if and only if $a=\pm b$
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
Situation: when a user self-marks their post as a duplicate, it shows as closed by "community" rather than the original poster.  Problems: this is not clear at all to most users of SE what has happened. It looks like the question was "mod closed" as a duplicate against the asker's wishes.    Suggestion: instead of the community user "closing" the post, have the final close user be the asker (or make it "Community &amp; Asker"). This will help clear up confusion and streamline the process for understanding what happens. How can I add "Show desktop" to the GNOME dash or Ubuntu Dock? In PHP, what does the ${$ } syntax do? What's a common interjection for the reaction to something creepy and disgusting (like some insects or spooky places, etc.)? Somebody asked me this question in a job interview and I replied that their joint distribution is always Gaussian. I thought that I can always write a bivariate Gaussian with their means and variance and covariances. I am wondering if there can be a case for which the joint probability of two Gaussians is not Gaussian? Allow horizontal scrolling of long math expressions Stack Exchange formats math, but often the formatted math is wider than the screen. It would be nice if formatted math were scrollable the same way that formatted code wider than the screen is scrollable. What's the derivative of: $ \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$? let $ y=\displaystyle \sqrt{x+\sqrt{{x}+\sqrt{x+\cdots}}}$, i'm really interesting to know how do I find :  $\displaystyle \frac{dy}{dx}$ ?.  Note: I have used the definition of derivative of the square root function but i don't succed .  Thank you for any help Is there any way to call the parent version of an overridden method? (C# .NET) In the code below I tried in two ways to access the parent version of methodTwo, but the result was always 2. Is there any way to get the 1 result from a ChildClass instance without modifying these two classes?  class ParentClass {     public int methodOne()     {         return methodTwo();     }      virtual public int methodTwo()     {         return 1;     } }  class ChildClass : ParentClass {     override public int methodTwo()     {         return 2;     } }  class Program {     static void Main(string[] args)     {         var a = new ChildClass();         Console.WriteLine("a.methodOne(): " + a.methodOne());         Console.WriteLine("a.methodTwo(): " + a.methodTwo());         Console.WriteLine("((ParentClass)a).methodTwo(): "          + ((ParentClass)a).methodTwo());         Console.ReadLine();     } }   Update ChrisW posted this:     From outside the class, I don't know   any easy way; but, perhaps, I don't   know what happens if you try   reflection: use the Type.GetMethod   method to find the MethodInfo   associated with the method in the   ParentClass, and then call   MethodInfo.Invoke   That answer was deleted. I'm wondering if that hack could work, just for curiosity. Why would someone use WHERE 1=1 AND &lt;conditions&gt; in a SQL clause (Either SQL obtained through concatenated strings, either view definition)  I've seen somewhere that this would be used to protect against SQL Injection, but it seems very weird.  If there is injection WHERE 1 = 1 AND injected OR 1=1 would have the same result as injected OR 1=1.  Later edit: What about the usage in a view definition?    Thank you for your answers.  Still, I don't understand why would someone use this construction for defining a view, or use it inside a stored procedure.  Take this for example:  CREATE VIEW vTest AS SELECT FROM Table WHERE 1=1 AND table.Field=Value I have been trying around different ranges of summations:  $$ \sum_{(m,n) \in \mathbb{Z}^2} \frac{m^2 - n^2}{(m^2 + n^2)^2} = 0$$  That's not any good.  What about if we restrict to $m, n \in \mathbb{Z}$ as positive integers.    $$ \sum_{m &gt; 0, n &gt; 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} = 0$$  Now here's an anti-symmetry.  I do not like taking out the symmetry, but perhaps I can ask about:   $$ \sum_{m &gt;  n &gt; 0} \frac{m^2 - n^2}{(m^2 + n^2)^2}  = \; ? \tag{$*$} $$  There doesn't seem to be a change of variables that can work.  And we've used symmetry about as much as we can.  This looks related to:  $$  \sum \frac{1}{n^2} = \frac{\pi^2}{6}$$  Perhaps this other series ($*$) also has a special value. Rooks on a 8 by 8 checker board. Probability problem Two rooks are placed on an 8 by 8 chessboard such that they're in different squares. What is the probability they can't attack each other? Rooks can attack each other if and only if they're in the same row or column. I know that there are questions like this but they give the general numbers not the probability I am not sure how to start the questions and I have looked at this questions for hours. Any help would be welcome. Starting iPhone app development in Linux? I've heard that you need to get a Mac if you want to develop iPhone apps. Is this true?   Is it possible to develop iPhone apps using Linux? If yes, what do I need and where do I download the necessary tools? Given that   $x^x = y$; and  given some value for $y$   is there a way to expressly solve that equation for $x$? How do I get back my suspend option in Gnome Shell? With the new version of Gnome Shell in Ubuntu 12.10 they turned  around by just displaying the shutdown option which becomes suspend on pressing Alt.  How do I get back my beloved suspend option? For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $ For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $  I just basically said that the gcd of a and b { written as C } obviously divides aZ and bZ, therefore it can be rewritten as  CdZ + CeZ -> C[dZ + eZ] -> CZ[d+e] where Cd=a and Ce=b.   if a and b and C are natural numbers, then  so are d and e. the sum of d and e is an integer, that when multiplied by an integer produces an integer. therefore  CZ[d+e] = CZ, so aZ + bZ = GCD(a,b)Z  { Where C is the gcd(a,b) } Spaces in variable assignments in shell scripts Examples and Counterexamples of Relations which Satisfy Certain Properties Definition: Given a set $X$, a relation $R$ on $X$ is any subset of $X\times X$.  A relation $R$ on $X$ is said to be  reflexive if $(x,x) \in R$ for all $x \in X$, irreflexive if $(x,x) \not\in R$ for all $x \in X$, transitive if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\in R$, intransitive (or antitransitive) if $(x,y) \in R$ and $(y,z) \in R$ implies that $(x,z)\not\in R$, symmetric if $(x,y) \in R$ implies that $(y,x) \in R$, antisymmetric if $(x,y) \in R$ and $(y,x) \in R$ implies that $x=y$.   Given any combination of the properties listed above, is there a nontrivial (i.e. nonempty) relation which satisfies that combination of properties? Noun form of "affected", meaning things that are affected by X Previous question:    That was when my buttons died.  On other days, my text dies.    And some times it's just italics.    Now, I like blaming @skiwi for this, and he's often nearby when it happens.  But today, he's not here, and it happened again.    I'm running Windows 8 and using Chrome 40.0.2214.94 m.  Refreshing and such does not fix the issue.  Inspect element -> console -> error log:  http://chat.stackexchange.com/chats/8595/messages/new Failed to load resource: the server responded with a status of 409 (Conflict) http://i.stack.imgur.com/2ZJdJ.png?s=128&amp;g=1&amp;g&amp;s=16 Failed to load resource: the server responded with a status of 502 (Bad Gateway) http://i.stack.imgur.com/boUZp.jpg?g&amp;s=16 Failed to load resource: the server responded with a status of 502 (Bad Gateway) http://i.stack.imgur.com/U8P3C.jpg?s=128&amp;g=1&amp;g&amp;s=32 Failed to load resource: the server responded with a status of 502 (Bad Gateway) http://i.stack.imgur.com/boUZp.jpg?g&amp;s=16 Failed to load resource: the server responded with a status of 504 (Gateway Time-out) http://chat.stackexchange.com/messages/19891816 Failed to load resource: the server responded with a status of 409 (Conflict)   What's going on here?  I should note, I can view italics by selecting, then alt-tabbing:    So it reeks of a client-side issue. What's hiding the text from me?  EDIT:  30 april 2015 it happened again =/ Possible Duplicate:          As answered in  I want to use git diff --color=always filename | less -r to get a colored output of my git diffs. Since I use this a lot it would be nice to set up an alias for this. But how to include the filename in this command?  I tried the following without success:  alias gdiff='git diff --color=always $1 | less -r'   Typing gdiff example.php displays the content of example.php with less but ignores the diff part.  Any ideas?