How to prove or disprove that $\{ 12x + 25y | x , y \in \mathbb{Z} \} = \mathbb{Z}$.
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
Is it possible to write a template that changes behavior depending on if a certain member function is defined on a class?  Here's a simple example of what I would want to write:  template&lt;class T&gt; std::string optionalToString(T* obj) {     if (FUNCTION_EXISTS(T-&gt;toString))         return obj-&gt;toString();     else         return "toString not defined"; }   So, if class T has toString() defined, then it uses it; otherwise, it doesn't. The magical part that I don't know how to do is the "FUNCTION_EXISTS" part. Creating node shapes What does f-stop mean? What does f-stop mean? Is it the same thing when people say "2 stops" for example? Window title in bottom of Activities overview is not visible when opening multiple windows We have a few Win32 applications (coded in Delphi 2006) where sometimes the user gets an error message saying "System Error. Code: 8. Not enough storage is available to process this command.".  From the stacktrace it looks like it is always during CreateWnd call  Main ($1edc): 004146cc +070 app.exe SysUtils               RaiseLastOSError 00414655 +005 app.exe SysUtils               RaiseLastOSError 004ce44c +130 app.exe Controls               TWinControl.CreateWnd 00535a72 +022 app.exe cxControls             TcxControl.CreateWnd 004ce82a +016 app.exe Controls               TWinControl.CreateHandle 00553d21 +005 app.exe cxContainer            TcxContainer.CreateHandle 00586ef1 +005 app.exe cxEdit                 TcxCustomEdit.CreateHandle 005c331d +005 app.exe cxDropDownEdit         TcxCustomDropDownEdit.CreateHandle 004ceaf0 +074 app.exe Controls               TWinControl.UpdateShowing 004ceb1e +0a2 app.exe Controls               TWinControl.UpdateShowing 004cebdc +03c app.exe Controls               TWinControl.UpdateControlState 004d118a +026 app.exe Controls               TWinControl.CMVisibleChanged 004cb713 +2bb app.exe Controls               TControl.WndProc 004cf569 +499 app.exe Controls               TWinControl.WndProc 004b727d +4c1 app.exe Forms                  TCustomForm.WndProc 004cb3a0 +024 app.exe Controls               TControl.Perform 004c9f6a +026 app.exe Controls               TControl.SetVisible 004b6c46 +03a app.exe Forms                  TCustomForm.SetVisible 004baf1b +007 app.exe Forms                  TCustomForm.Show 004bb151 +14d app.exe Forms                  TCustomForm.ShowModal 007869c7 +0d3 app.exe UfrmPrice      770 +19 TfrmPrice.EditPrice 0078655d +009 app.exe UfrmPrice      628  +0 TfrmPrice.actNewBidExecute 00431ce7 +00f app.exe Classes                TBasicAction.Execute 004c2cb5 +031 app.exe ActnList               TContainedAction.Execute 004c397c +050 app.exe ActnList               TCustomAction.Execute 00431bb3 +013 app.exe Classes                TBasicActionLink.Execute 004af384 +090 app.exe Menus                  TMenuItem.Click 004b059f +013 app.exe Menus                  TMenu.DispatchCommand 004b16fe +082 app.exe Menus                  TPopupList.WndProc 004b164d +01d app.exe Menus                  TPopupList.MainWndProc 004329a8 +014 app.exe Classes                StdWndProc 7e4196b2 +00a USER32.dll                     DispatchMessageA 004bea60 +0fc app.exe Forms                  TApplication.ProcessMessage 004bea9a +00a app.exe Forms                  TApplication.HandleMessage 004becba +096 app.exe Forms                  TApplication.Run 008482c5 +215 app.exe AppName        129 +42 initialization   I've never been able to get to the bottom of what causes this and as it happens fairly seldom I haven't been to concerned, but I would like to find out what causes it and hopefully rectify it...  EDIT: Full Stacktrace  EDIT 2: More info... The client who experienced this today has had my app installed for about 4 months and it is running on his PC 8 hours a day. The problem only appeared today and kept reappearing even though he killed my app and restarted it. None of the other apps on his system behaved strangely. After a reboot the problem goes away completely. Does this point towards the heap shortage that Steve mentions?  EDIT 3: Interesting msdn blog post  and  on the topic of the desktop heap. Though I'm not sure whether this is the cause of the problem it certainly looks likely. Is the function differentiable at $0$? Let $$f(x) = \begin{cases}\begin{align*}&amp;\cos{\dfrac{1}{x}}, &amp;x \neq0 \\ &amp;0, &amp;x=0. \end{align*}\end{cases}$$ Is the function $F(x) = \displaystyle \int_{0}^x f dx$ differentiable at $0$?  We can see that the function $f(x)$ is continuous everywhere except $x=0$. In order to show differentiability we will need to show the derivatives from the left and right are equal. So we need to show that $$\lim_{h \to 0^+} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^-} \dfrac{F(x+h)-F(x)}{h}.$$ The derivative from the right is $$\lim_{h \to 0^+} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^+} \dfrac{\displaystyle \int_{0}^x\cos{\dfrac{1}{x+h}}-\int_{0}^x\cos{\dfrac{1}{x}}}{h}$$ and the derivative from the left is $$\lim_{h \to 0^-} \dfrac{F(x+h)-F(x)}{h} = \lim_{h \to 0^-} \dfrac{\displaystyle \int_{0}^x\cos{\dfrac{1}{x+h}}-\int_{0}^x\cos{\dfrac{1}{x}}}{h}.$$ I am not sure how to proceed. The residue at $\infty$ I am stuck on the following problem :      $\,\,\,\,$*Problem*$\quad$The residue of an entire function at $\infty$ is $0$.      Solution: True. This follows from the definition of the residue at $\infty$ together with the Cauchy-Goursat Theorem. Another way to see this is to take the Taylor expansion for $f$ at $0$ $\displaystyle f(z)=\sum_{n=0}^\infty a_nz^n$ and replace $z$ with $1/z$ to get the Laurent expansion for $f(1/z)$ at $0$: $\displaystyle f(z)=\sum_{n=-\infty}^0a_{-n}z^n.$ Then we have that the residue at $\infty$ is given by the negative coefficient of the $1/z$ term of    $$ \dfrac1{z^2}f\left(\dfrac1z\right)=\sum_{n=-\infty}^{-2}a_{-n-2}z^n, $$   which is clearly $0$.   I am having trouble to understand the last few lines (in italic) in the given solution. Can someone give lucid explanation? Thanks and regards to all. Configure Postfix to use external MX servers for delivery of local mail if user is unknown I have a following setup:   linux box with postfix configured to be responsible for example.com domain domain's MX servers are configured so that mail sent to example.com is sent to google mail servers several user accounts on linux machine exist (same machine also hosts example.com site)   When someone from the outside attempts to send mail to address ending with @example.com, it gets routed to google mail (and there handled appropriately).  When linux machine tries to send mail to outside world, mail is delivered correctly, as reverse dns and spf records are configured correctly, so linux machine is valid mail sender for example.com domain (along with google mail servers).  However, here's the problem. When php application (hosted at linux box) tries to send mail to someuser@example.com (and someuser doesn't exist on linux box), it fails, since it doesn't even consult google mail servers, but postfix smtp locally concludes that "someuser" is unknown.  So, the question is: how do I tell postfix to relay mails sent to @example.com domain to google mail servers (so, to servers specified in MX records), IF and only if a mailbox is not found locally. Change the location of saved screenshot when screenshot taken by printscreen button in GNOME 3 Apply the latest Service Pack and Cumulative Update What is the difference between old style and new style classes in Python?  When should I use one or the other? Every nonzero element in a finite ring is either a unit or a zero divisor Check if a class is derived from a generic class I have a generic class in my project with derived classes.  public class GenericClass&lt;T&gt; : GenericInterface&lt;T&gt; { }  public class Test : GenericClass&lt;SomeType&gt; { }   Is there any way to find out if a Type object is derived from GenericClass?  t.IsSubclassOf(typeof(GenericClass&lt;&gt;))   does not work. hyperref: how to format text in a forms text-field I would like to pre-format the text in a form text-field, e.g. make it bold, italic or use a specific font. The following code generates a simple text-field:  \documentclass{scrreprt} \usepackage{hyperref} \begin{document} \textbf{The Text Field} \begin{Form} \TextField[]{\ } \end{Form} \end{document}   Is it possible to pre-format the text in the text-field? The hyperref package manual (10/2011) speaks of an optional parameter format and the use of JavaScript to format the field. Can this be used to format the text in the field? And if yes, how is it done? (I am not proficient in JavaScript) Git keeps prompting me for a password Where can I find a complete reference for the $PS1 variable? The default PS1 variable on my machine (Kubuntu 13.10) is this:  \[\e]0;\u@\h: \w\a\]${debian_chroot:+($debian_chroot)}\u@\h:\w\$   I'm looking for a reference for how the $PS1 variable works that, at a minimum, allows me to understand the above PS1 variable. Deriving the inverse of a 2x2 matrix I am looking for a derivation for the inverse of a 2x2 matrix. I am also wondering why the determinant is involved in the expression. I am familiar with high school maths and linear algebra. If there is an intuitive reason for expression i would also be interested in that. How do I change "Show Applications" button on GNOME 3 dash? I'm using Ubuntu with GNOME desktop.   I was wondering how to change the "Show Applications" button icon on the dash? What is an ultra-wide lens? What is the point at which a lens is considered "ultra-wide angle" vs just wide angle? Create a book cover with spine, rear page and flaps