Let $p$ and $x$ be two positive integers greater than 2. If it is given that the sum : $$1+x+x^2+x^3... x^{p -1}$$  is a prime, is it possible to prove or disprove that $p$ is prime? If so, what would this proof be?
Will be glad for a little hint: let x and n be positive integer such that $1+x+x^2+\dots+x^{n-1}$ is a prime number then show that n is prime
Map matching links and ideas? I'm using OpenStreetMap and its vectorial road network and I'd like to implement a map matcher algorithm.   Currently I'm able, for each GPS position, to retrieve the nearest road segment and calculate the projection of this position to that segment, like on this image (Red pin is the pure GPS position, in blue the mapped segment and in Green the mapped position):    However, due to the lack of accuracy of the GPS, sometimes the mapped position jumps from segment to another and can provide some inconsistent mapped position from time to time.  My current algorithm is very basic : from the pure GPS position, I get the nearest segment and decide that the mapped matched position is on this one. I know that this can be really improved.  I can imagine that taking the vehicle direction into account will improve the map matching but do you know any other approach that would enable me to improve my map matcher ?  I seek any link, and/or open source software? Let $G$ be a non-empty finite set with an associative binary operation so that cancellation law holds, i.e. $ab=ac$ or $ba=ca$ implies $b=c$, for any choices of $a,b,c$ in $G$. Assume that there is an identity element $e$ in $G$. Show that $G$ is a group.  Proof: To show $G$ is a group, conditions must hold. Suppose that $ab=ac$, then $b=eb=(a^{-1}a)b =a^{-1}(ab)=a^{-1}(ac) =(a^{-1}a)c=ec=c$. So left cancellation holds in $G$.  2) Suppose $ba=ca$, then $b=be=b(aa^{-1}) =(ba)a^{-1}=(ca)a^{-1} =c(aa^{-1})=ce=c$. So right cancellation holds in $G$.  3) If $a$ exists in $G$ then $aa^{-1}=a^{-1}a=e$, where $a$ is an inverse of $a^{-1}$. Since inverses are unique, $(a^{-1})^{-1}=a$.  4) Let $x$ be the inverse of $ab$. Then $(ab)x=e$. By associativity we have $a(bx)=aa^{-1}$. Through left cancellation we have  $bx=a^{-1}bx=ea^{-1}=b(b^{-1}a^{-1})$ and $x=b^{-1}a^{-1}$.  Thus $(ab)^{-1}=b^{-1}a^{-1}$. So all conditions hold, $G$ is a group.  Is this proof correct? I know to show $G$ is a group these conditions have to be met. This is all I have to show right? What are the SEO rules for HTML 5? What are the rules of engagement with respect to SEO in HTML 5?  Examples of things we have been mulling over with no conclusion:   Are you penalised for not using &lt;head&gt; and &lt;body&gt; tags? Do links in &lt;nav&gt; blocks get prioritised for follows? With &lt;aside&gt; (no bside though), &lt;section&gt;, &lt;summary&gt; and &lt;details&gt; which ones carry the most weight for content, one-liner descriptions and keyword tags are there search engine implications? If you use CSS to put a &lt;footer&gt; element at the top and a &lt;header&gt; element at the bottom (not that you would but it may be construed as such by an incomplete spider implementation)? Does the use of placeholder attributes on &lt;input&gt; show you are more user focused?   At the minute we are haphazardly pinning the content on the donkey with regard to tag usage but would be interesting to know if anyone has any insight into the "correct" tags to use with regards to SEO. Reprojected MODIS NDVI has range from -32768 to 32767, expected -1 to 1 File changed listener in Java Redirect parent window from an iframe action Determine a user's timezone Is there a standard way for a web server to be able to determine a user's timezone within a web page?   Perhaps from an HTTP header or part of the user-agent string? Minimal Sufficient Statistic for location family In Casella &amp; Berger Statistical Inference,in exercise 6.8, we're asked to prove that, for any distribution belonging to the location family, the order statistics are minimal sufficient.  How does one prove this? I have no idea on how to tackle this exercise.  Any help would be appreciated. How to override 'DefWndProc' in WPF What are good ways to make pdflatex output copy-and-pasteable? I have a Dell N5110 laptop with integrated Nvidia GeForce GT 525M and an Intel HD Graphics 3000 card; My problem is the default card is the Intel one, and it provides a very bad performance with Windows 8. So can I force to use the Nvidia one all the time including "Desktop Windows Manager" ? I´m having some trouble with my udev rule. At the moment, I had my udev rule setup to execute a script whenever a Android phone is connected to any USB port on the computer. But I don´t want the script to be executed from every USB port. I just want that the script to be execute in example when the phone is connected to the 4th USB port and nothing should happen when it is connected to 1st, 2nd or 3rd USB port.  How can I achieve that and how can I determine the for example 4th USB Port?  I would highly appreciate your help.  My current udev rule:  KERNELS="1-2:1.1", ACTION=="add", ENV{DEVTYPE}=="usb_device", ATTRS{idVendor}!="1d6b", ATTRS{idVendor}!="203a", ATTRS{idVendor}=="****", ATTRS{idProduct}=="****", RUN+="/usr/local/bin/tmp.sh $attr{serial}" What happens when you plug two sides of a cable to a single networking device? What is likely to happen when you plug two ends of a network cable to a single switch/router? Will this create problems on the network, or just be ignored? Currently, when flagging an off-topic question, the following choices are offered.   Questions about general computing hardware and software are off-topic for Stack Overflow. Questions concerning problems with code you've written must describe the specific problem and include valid code to reproduce it. Questions must demonstrate a minimal understanding of the problem being solved. Questions on professional server, networking, or related infrastructure administration are off-topic for Stack Overflow unless they directly involve programming or programming tools. Questions asking us to recommend a tool, library or favorite off-site resource are off-topic for Stack Overflow as they tend to attract opinionated answers and spam. This question belongs on another site in the Stack Exchange network   However, there are some questions that fit in none of these categories.  For example, career advice questions are off-topic here (and on programmers.SE), questions like  are off-topic on pretty much any SE site.    Some questions might also be relevant on another SE site not listed when the "belongs on another site" option is selected.  How should those questions be flagged?  Why isn't there a "it's off-topic because it is" option?  EDIT: just to be clear, I don't have the "Other" option under Off-Topic. I just found http://programmingfaq.w3ec.com/faq/4761/whats-the-hi-lo-algorithm which has an exact copy of this Stack Overflow question, , with all its answers and no difference in a single character. There is no reference to Stack Overflow.  Is this legal, or at least tolerated? Is this impertinent theft of information? I just can't see any sense in copying whole pages, particularly when not referencing the source. Proof that every metric space is normal Counting nodes in a tree in Java First of all, I swear this is not homework, it's a question I was asked in an interview. I think I made a mess of it (though I did realise the solution requires recursion). Here is the question:  Implement the count() method which returns the number of nodes in a tree. If a node doesn't have either a left or right child, the relevant getXXChild() method will return null  class Tree {    Tree getRightChild() {     // Assume this is already implemented   }    Tree getLeftChild() {     // Assume this is already implemented   }    int count() {     // Implement me   } }   My reason for asking the question is simply curious to see the correct solution, and thereby measure how bad mine was.  Cheers, Tony A reward becomes a penalty if I am working to build a reinforcement agent with DQN. The agent would be able to place buy and sell orders for a day trading purpose. I am facing a little problem with that project. The question is "how to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$".  I want to maximize the profit inside a trading day and avoid to place the pair (limit buy order, limit sell order) if the profit on that transaction is less than 100$. The idea here is to avoid the little noisy movements. Instead, I prefer long beautiful profitable movements. Be aware that I thought using the "Profit &amp; Loss" as the reward.  "I want the minimal profit per transaction to be 100$" ==> It seems this is not something that is enforceable. I can train the agent to maximize profit per transaction, but how that profit is cannot be ensured.  At the beginning, I wanted to tell the agent, if the profit of a transaction is 50 dollars, I will remove 100 dollars, then It becomes a penalty of 50 dollars for the agent. I thought it was a great way to tell the agent to not place a limit buy order if you are not sure it will give us a minimal profit of 100$. It seems that all I would be doing there is simply shifting the value of the reward. The agent only cares about maximizing the sum of rewards and not taking care of individual transactions.   How to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$? With that strategy, what guarantee that the agent will never make a buy/sell decision that results in less than 100 dollars profit? Does the sum of reward - # transaction * 100 can be a solution? I don't know much more about SEO, but it's interesting to learn about it. When I tried to search my website with an associated keyword or you can say with the exact name of the domain, I got some suggestions by Google. Here's .  First of all, I don't want to spamming here, I just want prove my question and want to give a hint about what I am talking here. The above link display the Did You Mean, I know the specific reason why Google shows this, but I want to know the Google's guidelines and some guidance by you experts so that if someone search for the particular keyword then Google hide that Did You Mean and display the result. Variable importance from GLMNET