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Probability question of hats How can I prove that $2017 \mid 1^{2017}+2^{2017}+\dots+2017^{2017}$? I tried proving it with the use of modulo, however it was to no avail. Afterwards, I  tried researching, for possible theorems, that may help, but that bore no fruit, either. Can you guys please help me proving it, as I am stuck? Thanking you in advance. Java : How to determine the correct charset encoding of a stream Working on a future method to post values to external web service. But since there is a limit of 50 callouts per invocation, I am getting error "Too many future calls : 51". Cases are loaded into salesforce from external ETL in bulk. So is there a way to workaround this error.   Class  public with sharing class caseTrigger {      //method invoked by trigger after insert     public void CaseInsert(List&lt;Case&gt; caseIns){           list&lt;Id&gt; caseIds = new list&lt;id&gt;();             List&lt;Case&gt; caseList = [Select id from case WHERE Id IN :caseIds];                 for(Case c : caseList){                     if(c.Status != 'closed'){                         caseIds.add(c.id);                     }                          if(f.caseId_User.size()&gt;0){PostCases(caseIds);}      }     //postCases (future method)     @future(callout = true)     public static void PostCases(List&lt;Id&gt; Ids){         //prepare Json to post to webservice    } } How can I respawn the Ender Dragon? Modular exponentiation by repeated squaring I have been stuck for several days on this old Analysis problem (I am doing some study on my own).  I have tried several things (which I'll indicate below), but I cannot seem to figure it out.  Here is how the problem is presented: Problem: &quot;Let $f$ be a continuous real-valued function on $[a,b]$.  Suppose there exists a constant $M \geq 0 $ such that $$|f(x)| \leq M \int_a^x |f(t)| dt$$ for all $x \in [a,b]$.  Show that $f(x)=0$ for all $x \in [a,b]$.&quot; My Thoughts: I have tried using the mean value theorem iteratively, but that seems to always lead me down a dead end road.  I deduced that $f(a)=0$.  If only $f$ were assumed to be differentiable, then maybe I could play with trying to get the derivative to be $0$, but unfortunately it's only continuous.  My other thought was to (somehow) use the condition to show that $\int_a^b |f(x)| dx = 0$.  I also played around a bit with contradiction, but to no avail.  Even if one of these hair-brained thoughts is correct, I am not really sure what to do next. If you have any ideas, suggestions, or solutions, I would really appreciate it if you are willing to share them.  Thank you for your time. CodeIgniter Anchor error: URL not found on this server XPath select node with namespace Let $A$ and $B$ be $m \times n$ and $n \times m$ real matrices.  I proved that if $\lambda$ is a nonzero eigenvalue of the $m \times m$ matrix $AB$ then it is also an eigenvalue of the $n \times n$ matrix $BA$. But I am having trouble finding an example showing that this need not be true if $\lambda=0$  Thank you in advance Travelling by bus A secretary with ____ good knowledge of English: "a" or no article? I'm trying to pass a test on "Articles exercise" as they call it . Reviewing my answers I got stuck about the two I posted on the picture below.  As I understand both words are uncountable (according to the ), so it looks like (or said for example ) I can't say a/an with an uncountable noun.  But this test says the opposite. Is there some trick? Or am I just dumb? Please help me to understand why I need to use "a" article in these cases?        We need a secretary with ____ good knowledge of English.          a  (marked as the correct answer)   the     a / the     no article is needed (the answer I think is correct)        We're having ____ terrible weather.         a (marked as the correct answer)     the     a / the     no article is needed (the answer I think is correct) Why does $\sum_{k=1}^{\infty}\frac{{\sin(k)}}{k}={\frac{\pi-1}{2}}$? Inspired by  (and far more straightforward, I am guessing), Mathematica tells us that $$\sum_{k=1}^{\infty}\dfrac{{\sin(k)}}{k}$$ converges to $\dfrac{\pi-1}{2}$.   Presumably, this can be derived from the similarity of the Leibniz expansion of $\pi$ $$4\sum_{k=1}^{\infty}\dfrac{(-1)^{k+1}}{2k-1}$$to the expansion of $\sin(x)$ as $$\sum_{k=0}^{\infty}\dfrac{(-1)^k}{(2k+1)!}x^{2k+1},$$ but I can't see how...  Could someone please explain how $\dfrac{\pi-1}{2}$ is arrived at? Why does "Size on disk" vary when "Size" does not with the same set of files? If you have a conducting hollow sphere with a uniform charge on its surface, then will the electric field at every point inside the shell be 0. The reason the electric field is 0 at the center is clear from the symmetry of the sphere, but for a point at a certain distance from the center, shouldn't a net electric field exist?  I saw a similar question on the site but it was vaguely explained. Can I still command/control concentration spells while in the Border Ethereal? If I have cast something like Animated Objects or Bigby's Hand and then follow up the next round with casting Etherealness, can I still command/control those spells? Circular References Cause Memory Leak? I'm trying to run down a memory leak in a windows forms application.  I'm looking now at a form which contains several embedded forms.  What worries me is that the child forms, in their constructor, take a reference to the parent form, and keep it in a private member field.  So it seems to me that come garbage-collection time:  Parent has a reference to the child form, via the controls collection (child form is embedded there).  Child form is not GC'd.  Child form has a reference to the parent form, via the private member field.  Parent form is not GC'd.   Is this an accurate understanding of how the garbage collector will evaluate the situation?  Any way to 'prove' it for testing purposes? How to force GPG to use console-mode pinentry to prompt for passwords? If $a > b$, is $a^2 > b^2$? Given $a &gt; b$, where $a,b ∈ ℝ$, is it always true that $a^2 &gt; b^2$? Is StringBuilder really faster than Aggreggate?