Solving $x^2 + y^2 = M$ with $M$ prime
Efficiently finding two squares which sum to a prime
Here's the information :     There are four different pairs of   opening and closing tags which can be   used in PHP. Two of those, &lt;?php ?&gt;   and &lt;script language="php"&gt; &lt;/script&gt;,   are always available. The other two   are short tags and ASP style tags, and   can be turned on and off from the   php.ini configuration file. As such,   while some people find short tags and   ASP style tags convenient, they are   less portable, and generally not   recommended.   In my experience most servers do have short tags enabled. Typing  &lt;?=   is far more convenient than typing  &lt;?php echo    The programmers convenience is an important factor, so why are they not recommended? Is it possible to have the dock in different positions in different desktop? Is it possible to have the dock in different positions in different desktops? In particular I'd like to change the settings between a normal desktop and a desktop where there's an app at full screen. In this way I'd keep the dock in lower side of the desktop when there's an app at full screen and vertically on the left side during normal use.  I have this problem that, sicne I usually have the dock vertically on the left, it pops out everytime i go to the far left in an app I'm using with full screen, and using this app I have to move the mouse to the left quite often. What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it. Can I programmatically open the devtools from a Google Chrome extension? Can I run an HTTP GET directly in SQL under MySQL? I'd love to do this:  UPDATE table SET blobCol = HTTPGET(urlCol) WHERE whatever LIMIT n;   Is there code available to do this? I known this should be possible as the  include an example of adding a function that does a DNS lookup.  MySQL / windows / Preferably without having to compile stuff, but I can.  (If you haven't heard of anything like this but you would expect that you would have if it did exist, A "proly not" would be nice.)  EDIT: I known this would open a whole can-o-worms re security, however in my cases, the only access to the DB is via the mysql console app. Its is not a world accessible system. It is not a web back end. It is only a local data logging system $A^A$ in category of graphs (reference is Lawvere/Schanuel, Session 31, Ex. 1)  I'm trying to calculate the exponential object $A^A$ and its evalution map $e \colon A \times A^A \to A$ in the category of graphs, where $A$ is the "arrow graph" (ie. one arrow and two dots).  In the following, $D$ is the graph with one dot and no arrows, $1$ is the terminal object in this category (graph with one dot and one arrow, the loop).  So far I have:   The points of $\mathbf{1}\to A^A$ correspond to the maps $A\to A$ (via two standard isomorphisms), and since $\mathbf{1}$ is the loop, and there is one map of graphs $A \to A$, there is one loop in $A^A$. The dots $D\to A^A$ correspond to the maps $A \times D \to A$, of which there are four, hence four dots in $A^A$. The arrows $A \to A^A$ correspond to the maps $A \times A \to A$, of which there are four, hence four arrows in $A^A$.   But I'm stuck on how to put these together to constitute $A^A$ and its evaluation map. What is the black thing on the circuit What is the black thing on the below circuit?   Is it used to hide the IC (or other components) that is used on the circuit?   What material is it? CakePHP View including other views I have a CakePHP application that in some moment will show a view with product media (pictures or videos) I want to know if, there is someway to include another view that threats the video or threats the pictures, depending on a flag. I want to use those "small views" to several other purposes, so It should be "like" a cake component, for reutilization.  What you guys suggest to use to be in Cake conventions (and not using a raw include('') command) I have passed the calc sequence, and thought that I understood things.  But I have trouble with limits now and again.  From the way I understand it, the 'best' way to evaluate a limit, is to evaluate the expression at the number in the limit.  In that way it's not only a limit, but an algebraic expression (so, I think, the need for limits goes away entirely, superseded by accuracy.)  But then I see something like $\lim_{x\to 2} \frac{x^2-4}{x-2}$.  Now, I think in my mind 'the best way to evaluate this is just to plug in $2$'  But it doesn't work that way, as the limit is $4$, and if I plug in, the answer is $0/0$.  I think that people here, with their natural talent in math, can perceive where my train of thought is going wrong, and correct me.  Please! Use second argument for optional first argument if not provided in macro I'm trying to construct a command with one optional and one mandatory argument and I'd like the default if the optional argument is not provided to be #2.   Why does this not work?  (error: Illegal parameter number ...)  \documentclass{article}  \newcommand{\mycommand}[2][#2]{\label{#1}#2} \begin{document} \mycommand{mytext} \end{document}   And what would be a way around it?   EDIT: For clarification of my specific use case: I'm trying to define a command that passes a variable on as an option to an environment along those lines, where myenv can have options like optionone=X or optiontwo=Y so the default for the optional #1 should be optionone=#2 (not literally #2).   \newcommand{\mycommand}[2][optionone=#2]{\begin{myenv}[#1]\input{#2}\end{myenv}}   Maybe there's generally a better approach?   (The environment definition I'm using is from .) We want to encrypt / encode URL parameters on our pages. I tried to encrypt a parameter using  with AES algorithm as explained in the   %%[SET @encData=EncryptSymmetric("test", "AES", @null, "1111", @null, "0000000000000000", @null, "00000000000000000000000000000000") ]%% AES: %%=v(@encData)=%%   The result of this function is      AT1r0irnzM+Ax1j8zN+zAw==   Then I tried to decrypt the value using an , but I always received an error message.  I suppose there is a difference between AES algorithm in Marketing Cloud and AES used in the online tool. Indeed if I encrypt the same word with an online tool (128-bit), I received this result      l4Yo3sFofFD1EMmtoh397w==   Do you have any deep information regarding this function? What could be the difference? Re-Structuring a JSON Borel-Cantelli-related exercise: Show that $\sum_{n=1}^{\infty} p_n < 1 \implies \prod_{n=1}^{\infty} (1-p_n) \geq 1- S$. This is supposed to be related to the  (my justification for the independence tag). In Williams' Probability with Martingales, 2BCL is proven and then the following is given as an exercise:  Prove $S \doteq \sum_{n=1}^\infty p_n &lt; \infty \implies \prod_{n=1}^\infty (1-p_n) &gt; 0$ assuming $0 \leq p_n &lt; 1$. Hint: Show that $S &lt; 1 \implies \prod_{n=1}^\infty (1-p_n) \geq 1 - S$.   Proving the hint: I tried to find $\{a_n\}$ s.t. $$\prod_{n=1}^\infty (1-p_n) \geq \prod_{n=1}^\infty e^{a_n} = e^{\sum_{n=1}^\infty a_n} \geq 1 - \sum_{n=1}^\infty a_n \geq 1 - S &gt; 0$$ That is, find $\{a_n\}$ s.t.: 1a. $1 - p_n \geq e^{a_n}$ 1b. $a_n \leq p_n$ I thought of $a_n = \ln(1-p_n)$ (a reason why $p_n &lt; 1$, I guess) Is that right? Edit: Actually, assuming my proof is right, is $S &lt; 1$ used in the proof? If so, where?  From Williams book: I have a command that I want to have run again automatically each time it terminates, so I ran something like this:  while [ 1 ]; do COMMAND; done;   but if I can't stop the loop with Ctrl-c as that just kills COMMAND and not the entire loop.  How would I achieve something similar but which I can stop without having to close the terminal? How general is the Lagrangian quantization approach to field theory? How to use "`" in the same way it is used on the SE websites? The app forgets that I voted when I scroll the question Let $G$ be a finite group, say a group with $n$ elements, and let $\emptyset \neq S \subseteq G$. Suppose $e \in S$, and that $S$ is closed with respect to multiplication. Prove that $S$ is a subgroup of $G$.    Let $G = \{a_1, \ldots, a_n\}.$ Let $a_i \in G.$ Then any number of $a_ia_1, a_ia_2, \ldots, a_ia_n \in S,$ since $S$ is closed under multiplication. One of those $a_ia_j$ is $e$ since $e \in S.$ Then either $a_i$ or $a_j$ is $a^{-1}.$ Would this argument work? abhigenie92@ubuntu:~$ (sleep 2; echo $BASH_SUBSHELL ;sleep 2) 1 abhigenie92@ubuntu:~$ (sleep 2; echo $BASH_SUBSHELL ;sleep 2)&amp; [1] 3297 abhigenie92@ubuntu:~$ 1  [1]+  Done                    ( sleep 2; echo $BASH_SUBSHELL; sleep 2 )   What happens when launch it as a background process, why don't I get the prompt back and I have to press Enter? In both cases it launches a child shell. Why is $\mathbb{R}^2$ not a subspace of $\mathbb{R}^3$? I cannot understand why $\mathbb{R}^2$ is not a subspace of $\mathbb{R}^3$.   My reasoning is as follows: Choose any elements $v_1$ and $v_2$ from $\mathbb{R}^2$, add them together you get an element of $\mathbb{R}^2$ and same for scalar multiplication and $0$ vector is an element of $\mathbb{R}^2$. So where did I go wrong?