How can I solve this Diophantine equation: $$(n-1)!+1=n^m$$ with $n,m$ positive integers?  From Wilson's theorem we can note that $n$ is a prime number. I proved to rewriting the equation as:$$(n-2)!=n^{m-1}+n^{m-2}+....+1$$ but in vain. I proved to solve also through the theorem LTE bur I analysed only some cases without obtain a general solution.
How to find all positive integers $n$ such that $(n-1)!+1$ can be written as $n^k$ for some positive integer $k$?
How to prove sum of powers property of roots of unity? We know that $1+\alpha_1+\alpha_2+...+\alpha_{n-1}=0$ where $\alpha_i$ are the roots of $z^n=1$. How can I prove that: $$1+\sum_{i=1}^{n-1}\alpha_i^m=\begin{cases}0\quad m\in Z,m\not\equiv0\pmod n\\n\quad m\in Z,m\equiv0\pmod n\\\end{cases}$$ Once a lead is converted it automatically creates an account, contact and one opportunity. But in my case i want to display the result without creating an Account. Please provide me with a sample code.  Any help will be appreciated... I googled it but I couldn't find the answer... maybe I didn't seek it in the proper way. My question is if &quot;to&quot; must be repeated in sentences such as the following ones:   In the past, women used to do the housework and to take care of children.  The aim of this meeting is to control their progress and to discuss the new working plan.    If I had to bet, I would omit the second to... But I am not sure about it. CLI path to ftp network connection I've setup a connectio to an FTP server in Nautilus / Nemo / Caja, the file manager. Now I can browse the contents via this file manager.  How can I browse these files via the command line? What is the path to this network connection? Is this possible, is this a system connection, or specific to the file manager, and do I have to setup a separate FTP connection to do that? If I open this connection in Caja, I see it in Nemo as well, so it seems like a system connection. Do black holes have a moment of inertia? My question is in the title: Do black holes have a moment of inertia?  I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the literature. "Baggage" versus "luggage" I have the feeling that luggage is more closely associated with vacation travel, whereas baggage is for general transportation.  Or... are they just exact synonyms? Why cannot fermions have non-zero vacuum expectation value? In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermions to take vevs? Determine if Term has Grandparent/Great-Grandparent I found the following blog title without a question mark from :     How to ease Afghanistan’s progress in cricket   Is it grammatical, if we don't put question mark in questions of titles? I think this blog title should have been like this:     How to ease Afghanistan’s progress in cricket?   I also found the following blog title from  without a question mark:     Election rigging 101: How to steal a mandate   However, I found a question mark from other blog title of :     Elections 101: What is the ECP and what does it do on election day? How does the Adam method of stochastic gradient descent work? Evaluation of $ \sum_{k=0}^n \cos k\theta $ I just wanted to evaluate  $$ \sum_{k=0}^n \cos k\theta $$  and I know that it should give  $$  \cos\left(\frac{n\theta}{2}\right)\frac{\sin\left(\frac{(n+1)\theta}{2}\right)}{\sin(\theta / 2)}   $$  I tried to start by writing the sum as  $$ 1 + \cos\theta + \cos 2\theta + \cdots  + \cos n\theta $$  and expand each cosine by its series representation. But this soon looked not very helpful so I need some clue about how this partial sum is calculated more efficiently ... I try to download a file with wget and curl and it is rejected with a 403 error (forbidden).  I can view the file using the web browser on the same machine.  I try again with my browser's user agent, obtained by . I do this:  wget -U 'Mozilla/5.0 (X11; Linux x86_64; rv:30.0) Gecko/20100101 Firefox/30.0' http://...   and  curl -A 'Mozilla/5.0 (X11; Linux x86_64; rv:30.0) Gecko/20100101 Firefox/30.0' http://...   but it is still forbidden. What other reasons might there be for the 403, and what ways can I alter the wget and curl commands to overcome them?  (this is not about being able to get the file - I know I can just save it from my browser; it's about understanding why the command-line tools work differently)  update  Thanks to all the excellent answers given to this question. The specific problem I had encountered was that the server was checking the referrer. By adding this to the command-line I could get the file using curl and wget.  The server that checked the referrer bounced through a 302 to another location that performed no checks at all, so a curl or wget of that site worked cleanly.  If anyone is interested, this came about because I was reading  page to learn about embedded CSS and was trying to look at the site's css for an example. The actual URL I was getting trouble with was  and the curl I ended up with is  curl -L -H 'Referer: http://css-tricks.com/forums/topic/font-face-in-base64-is-cross-browser-compatible/' http://cloud.typography.com/610186/691184/css/fonts.css   and the wget is   wget --referer='http://css-tricks.com/forums/topic/font-face-in-base64-is-cross-browser-compatible/' http://cloud.typography.com/610186/691184/css/fonts.css   Very interesting. Why square the difference instead of taking the absolute value in standard deviation? In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute value of the difference instead and get the expected value (mean) of those, and wouldn't that also show the variation of the data? The number is going to be different from square method (the absolute-value method will be smaller), but it should still show the spread of data. Anybody know why we take this square approach as a standard?  The definition of standard deviation:  $\sigma = \sqrt{E\left[\left(X - \mu\right)^2\right]}.$   Can't we just take the absolute value instead and still be a good measurement?  $\sigma = E\left[|X - \mu|\right]$ Follow a question I've come across a few interesting questions over the last few months on Stack Overflow. They're not necessarily questions I need an answer to, but the questions are nonetheless very interesting, and now I want to know what the answers are.  I don't want to add this question to my favourites because I have my really handy posts in there.   Ideally I would like to have another kind of shortlist to which I can add these posts. I would get notifications just as if it were my own post, without having these as favourites.  What do you think of that? It would be available only for questions, and you would receive notifications just like the author, for new answers and comments on the question (not comments on the answers).  You could browse the posts you're following, as well as stop following them.   The thing is sometimes I come across a semi interesting question and upvote and maybe even comment, but I never hear about it again, because sometimes it's just not interesting enough to remember.  Like I said in the comments, I don't feel like the favourite list is really for this. I want in-your-face red dot notifications for new answers on brand new interesting questions I find. The favourites is for that post with an answer that you know you'll need again. Send urgent mail in Gmail Is it possible to set the "urgent" flag in Gmail for outgoing mail? I'd like to be able to flag time-sensitive emails as such. Why was the Triwizard Cup used as the portkey? How to remove blank lines from a file (including tab and spaces)? I want to remove all empty lines from a file. Even if the line contains spaces or tabs it should also be removed. I'm starting to write a book on . Since I've been contributing on this tag for a long time, I had the opportunity to read &amp; answer several interesting threads on Stackoverflow related to this technology.  I would like to discuss some of the interesting cases published on Stackoverflow in my book, and I wonder if I could use the images and code shared on those threads in it.  I'm hoping somebody from StackExchange could clarify about the copyright status of the material shared on Stackoverflow questions/answers. When & why I need to use web.AllowUnsafeUpdates = true How do I pack textures for sending off to a render farm Whenever i try to send a project off to a render farm such as sheepit, it says it needs the textures packing with the file in order to render correctly.  How would I do this?