The equation $x^2=a$ in a finite group $G$ of odd order.
What finite groups always have a square root for each element?
I have a question on Holder space.Is the space $C^2(\mathbb{R}^n)$ embedded in $C^{1,\alpha}(\mathbb{R}^n)$? I think in the bounded domain case, this should be true. But what if in the case where the domain is not bounded? Thanks for any hint! In Catan, can you continue a "circular" road? If I have 6 roads that go all around a single hex tile, they are a continuous uninterrupted road (assuming none of my opponents interrupts it with their settlements/cities). But, can I continue this 6-piece road and create a 7-piece continuous road by building a road that goes out of this hex tile? Here's an image of what I'm talking about:    Is this a valid 7-piece continuous road? Redirect all subsequent commands' stderr using exec How is the width of a slit related to the intensity of light passing through it? Here's a question I got in my final exam this morning. &quot;If in Young's double-slit experiment setup, the ratio of the intensity of the bright spot to the dark spot is 25:9, what is the ratio of the width of the slits?&quot; Here's what I did. Since the ratio of intensity at the bright and dark spots is 25:9, the ratio of amplitudes there must 5:3. Which means the amplitude of one wave is 4 times the other. Now, knowing that the amplitude of light through the wider slit is 4 times the amplitude of light through the narrower slit, how can I determine the ratio of the slits' width? Escaping HTML strings with jQuery Does anyone know of an easy way to escape HTML from strings in ?  I need to be able to pass an arbitrary string and have it properly escaped for display in an HTML page (preventing JavaScript/HTML injection attacks).  I'm sure it's possible to extend jQuery to do this, but I don't know enough about the framework at the moment to accomplish this. Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties Prove or disprove that,     There always exists a solution of the equation, $$n^m=x^2+py^2$$ with odd $x$ and $y$ and for all $m\geq k$ for some positive integral $k$. Here $p$ is an odd prime and $n\in 2\mathbb{N}$. Is $k$ dependent on $n$? If so then find a way to calculate the value of $k$.   This is basically one of my conjecture which I am trying to prove for quite sometime. Unfortunately, I have progressed very little in this problem. So far I have been only able to prove that for all $m\geq3$ , $n=2$ and $p=7$ there is always a solution of the equation meeting the constraints.   Any idea how to tackle the problem?    Update  After D. Burde's answer of the original problem (see below) I am now interested in finding all $(n,m,p)$ triplets such that the equation holds. Any ideas regarding this problem? Ambiguity in Negation: "John did not come because of the rain" Trying to understand formula for counting regions of hyperplane arrangements in $\mathbb{R}^2$ There are up to $\binom{n}{2} + n + 1$ regions created by a hyperplane arrangement in $\mathbb{R}^2$ containing $n$ hyperplanes.  I want to understand this in a demonstrative way. Each hyperplane splits each region it passes in two regions. A newly added hyperplane therefore creates a new region each time it crosses another hyplerplane or the plane. So the number of regions should be $1$ (plane) $+ \binom{n}{2}$ (number of intersections of $n$ lines). But as I know the answer, I know that I am missing $n$ regions.   Do you know where my mistake is? Why do I have to add the number of lines to get the max. number of regions? Dealing with bundle/omnibus/list-of-questions question that consists of rather distinct questions I have looked at the various help pages but I couldn't find a clear guideline for the following issue: often enough someone will ask in the same post (i.e. in the same SE-question) a whole bunch of questions (in the plain English sense of the word), which while may be about the same topic are nevertheless sufficiently distinct that each may require several paragraphs of text to answer adequately.   I can see an upside for leaving related questions grouped together from the asker's perspective: "there's a thread (on SE) answering all my questions about topic T!" On the other hand, from the perspective of organizing questions by having a clear heading/title for each (actual) question and so forth, i.e. from the perspective of SE being a fairly structured database of Q&amp;As instead of being a more like a collection of forum threads "I'm confused about topic T", the omnibus question-list approach seems clearly sub-optimal.  The omnibus approach also makes the issue of accepting answers (and perhaps reviewing such actions) difficult: if two different users give replies to different parts/sub-sets of the question-list, which one is the most adequate one? Even upvoting all partial answers seems iffy because it actually penalizes the user(s) who provides(s) the most complete answer to the question-list: since a user can only give at most one upvote to another user's answer, if user X provides answers to A &amp; B in the same SE-answer, he can only get at most one upvote from user Y, whereas if these were two different SE-answers, he could get two upvotes from user Y.  So, given the above problems, which I think are real enough, is there anything in the SE system addressing list-of-questions question splitting? Interpreting the residuals vs. fitted values plot for verifying the assumptions of a linear model I was just wondering how can you use "there is" followed by a word that is in plural, e.g  "There's cupcakes in the fridge"  and  "There is a couple of things we can do --"   Is it just slang? Ubuntu 12.04 boots to TTY1 Why the names Type 1, 2 error? Can I put a metal safe weighing 2000 lbs in a 12x12 room? I have a 12'x12' upstairs bedroom. Can a 2000 lbs safe be placed in that room? The dimensions would be the same size as a queen size bed (60"x80").  Can you supply the math in your answer.  Thank you in advance  Danny Extended sound of thunder "Awesome" vs. "Awful" How to create a permanent "alias"? If you create an alias for example:   alias cls="clear"   It exists untill you kill terminall session. When you start a new terminal window the alias doesn't exist any more. How to create "permanent" alias, one that exists in every terminal session? I am in the middle of a problem and having trouble integrating the following integral:  $$\int_{-1}^1\frac1{(1+x^2)^2}\mathrm dx$$  I tried doing partial fractions and got:  $$1=A(1+x^2)+B(1+x^2)$$  I have no clue how to solve this since it is obvious there is no way to cancel out either $A$ or $B$ to get the other variable. Please guide me.  Thank you. I hope someone can help me.  I am currently on holiday for 3 months in America under the Visa Waiver Program and would like to stay an extra 2 or 3 weeks. I know I will have to leave the country, renew my visa waiver and then reenter and so wanted to know if I will have an issue reentering.  I will only be out of the country for about 24 to 48 hours, just enough to renew the visa and get on a plane. I understand it is up to the border control person on the day, but does anyone think I will have an issue?? How do I transition to SSL without affecting PageRank?