Prove $ n \equiv s(n)\ ($mod$\ 3)$ using the fact that $\ [10^n] = [1]$.
Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)
Is there any way to create a simple txt file without opening the terminal? Is there any way to create a text file without using the terminal at all? I'm looking for a word that applies to all the things a person can wear, e.g. clothes, shoes, accessories, etc. It musn't be too generic, e.g. product, item, etc. How would you show that if $ac≡bc$ $\mod m$ and $\gcd(c,m)=d$, then  $a≡b$ $\mod \frac{m}{d}$?  Any help would be much appreciated! How to line up the pieces at the coast near the shipwreck? In The Witness, I was walking along the coast, and I came upon this:    Now, since I've learned      that mazes can be embedded in the environment,   I see the puzzle here, but I just can't get the pieces to line up well enough.  Standing on the couch and walking all around it doesn't seem to get me a       functional maze.   Where do I need to stand to activate the puzzle successfully? Error "WIF10201: No valid key mapping found" when trying to create claims from SAML What does env x='() { :;}; command' bash do and why is it insecure? There is apparently a vulnerability (CVE-2014-6271) in bash:   I am trying to figure out what is happening, but I'm not entirely sure I understand it. How can the echo be executed as it is in single quotes?  $ env x='() { :;}; echo vulnerable' bash -c "echo this is a test" vulnerable this is a test     EDIT 1: A patched system looks like this:  $ env x='() { :;}; echo vulnerable' bash -c "echo this is a test" bash: warning: x: ignoring function definition attempt bash: error importing function definition for `x' this is a test   EDIT 2: There is a related vulnerability / patch:  which uses a slightly different test:  $ env 'x=() { :;}; echo vulnerable' 'BASH_FUNC_x()=() { :;}; echo vulnerable' bash -c "echo test"   unpatched output:  vulnerable bash: BASH_FUNC_x(): line 0: syntax error near unexpected token `)' bash: BASH_FUNC_x(): line 0: `BASH_FUNC_x() () { :;}; echo vulnerable' bash: error importing function definition for `BASH_FUNC_x' test   partially (early version) patched output:  bash: warning: x: ignoring function definition attempt bash: error importing function definition for `x' bash: error importing function definition for `BASH_FUNC_x()' test   patched output up to and including CVE-2014-7169:  bash: warning: x: ignoring function definition attempt bash: error importing function definition for `BASH_FUNC_x' test   EDIT 3: story continues with: Browsing folders with more than 100000 images How to change material's color in blender game engine? Is it possible to create individual power settings for each hard drive? I have a number of different drives that I use for different purposes but I only use two of them frequently. I would like for the others to enter sleep mode when not in use, but never my main two.  Is there any way to edit power saving settings for individual drives? Currently I am using Outlook 2010, and sometimes customers claim that they will received an attachment in Windows.dat format.  I have searched online for possible solutions, but mostly the suggestion is to change the sending format to plain text. However, by using plain text format, there is some limitation.  So I just wonder, besides the plain text format, is there a ways to solve the winmail.dat issue?  Besides, does plain text format really 100% avoid the issue? external variable in awk How to edit Parameters for an Object after it is created? When you first add a cylinder, you have the option to change the number of vertices, etc, but once you do anything else in blender, it seems you no longer can edit those parameters.   Is there a setting anywhere or an add-on that allows these parameters to be edited later on? If not, how easy would such an addon/feature be to create for anyone reading this? Suppose $f$ is continuous on $[a,b]$ and differentiable on (a,b). Does it follow that $f'$ is continuous on $(a,b)$? How do I use reflection to call a generic method? What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod&lt;T&gt;() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod&lt;T&gt;()?         GenericMethod&lt;myType&gt;(); // This doesn't work          // What changes to call StaticMethod&lt;T&gt;()?         Sample.StaticMethod&lt;myType&gt;(); // This also doesn't work     }      public void GenericMethod&lt;T&gt;()     {         // ...     }      public static void StaticMethod&lt;T&gt;()     {         //...     } } What is -crf used for in ffmpeg When converting an array of jpegs to a video file (ogg format) I have been using the -crf option.  What are the valid ranges for -crf? Currently I am using 23.    I cannot find the bookmark I read to know what this flag does and I have spent some time Googling around.  These are the arguments I am using at the moment:  -f image2 -r 10 -i " + _sourcePath + @"\img%05d.jpg -crf 18  -y -r 10 " + _destPath + "\\" + _filename + ".ogg" Euclidean Algorithm for GCD of polynomials I am struggling to use the Euclidean algorithm for polynomials.  Given something like $$GCD(x^5+1, x^3+1)$$  I can easily use it as follows:   $$x^5+1 = x^2(x^3+1) -x^2 +1 \\ x^3+1 = -x(-x^2+1) + x +1 \\ -x^2+1 = (x+1)(-x+1)$$  GCD = x+1  But for something like $$GCD(2x^2+6x+3, 2x+1)$$   I cannot figure out how to do it using the same method. I start like this:  $$2x^2+6x+3 = x(2x+1) + 5x+3\\ 2x+1 = \frac{2}{5}(5x+3) - \frac{1}{5}\\$$  and I am not sure how to continue. Any help would be appreciated, sorry for my poor attempt at using LaTeX. I often find myself in a situation where I am facing multiple compilation/linker errors in a C++ project due to some bad design decisions (made by someone else :) ) which lead to circular dependencies between C++ classes in different header files (can happen also in the same file). But fortunately(?) this doesn't happen often enough for me to remember the solution to this problem for the next time it happens again.  So for the purposes of easy recall in the future I am going to post a representative problem and a solution along with it. Better solutions are of-course welcome.     A.h  class B; class A {     int _val;     B *_b; public:      A(int val)         :_val(val)     {     }      void SetB(B *b)     {         _b = b;         _b-&gt;Print(); // COMPILER ERROR: C2027: use of undefined type 'B'     }      void Print()     {         cout&lt;&lt;"Type:A val="&lt;&lt;_val&lt;&lt;endl;     } };       B.h  #include "A.h" class B {     double _val;     A* _a; public:      B(double val)         :_val(val)     {     }      void SetA(A *a)     {         _a = a;         _a-&gt;Print();     }      void Print()     {         cout&lt;&lt;"Type:B val="&lt;&lt;_val&lt;&lt;endl;     } };       main.cpp  #include "B.h" #include &lt;iostream&gt;  int main(int argc, char* argv[]) {     A a(10);     B b(3.14);     a.Print();     a.SetB(&amp;b);     b.Print();     b.SetA(&amp;a);     return 0; } Is Bezout's lemma enough to confirm the GCD of a number. Is Bezout's lemma enough to confirm the GCD of a number?  So suppose we have $$ax+by=z$$ does this mean $$\gcd(a,b)=z$$ single query to print all the rows whose count is greater than 10 Drawing line less than one pixel thick requires anti-aliasing in Android 4.2