While messing with modulus in python,  lomod = [num % 27 for num in [i * 8 for i in range(27)]]   print('Unsorted:', lomod)   lomod.sort()   print('Sorted:', lomod)  I found something interesting. For $a,b\in\mathbb{Z}$, and $a,b$ are relatively prime, and $0 \le x &lt; b$, $A =ax\mod b$, then $A = \{0,1...,b-1\}$ with no repeating integers. For example in the case of $a = 8, b=27$, for values of $x$ such that $0\le x &lt; 27$ $A =8x\mod27$ ,  then $A =$ [0, 8, 16, 24, 5, 13, 21, 2, 10, 18, 26, 7, 15, 23, 4, 12, 20, 1, 9, 17, 25, 6, 14, 22, 3, 11, 19] sorted, $A =$ [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26] Which contains all values from $0$ to $26$ once. However, I don't know how to prove this generally. Is there anyone that can help me?
How can I prove that $\,ax\equiv b\pmod{\! n}\,$ has a unique solution if $\,\gcd(a,n) = 1$?  I suspect that the Bezout identity for $\,\gcd(a,b) = 1$ is the key but I don't see how to proceed.
Where to locate "sockets" I am new to this, so sorry if its obvious. I am running a Debian server and installing the likes of UWSGI, NGinx etc on there. The configurations keep talking about pointing to "sockets".  In the build options I seem to be able to specify where the sockets for each program go. By default it looks like most of them go in /tmp (not all of them).  Is this a good place for them to go? I'm trying to keep things as organized as possible but just bunging them in /tmp doesn't seem like the best option. Rigor in quantum field theory Do photons have acceleration? window-switching keyboard shortcuts interfere with emacs and cannot be changed in the main keyboard system preferences Unicoin Bug: Automining Returns Diminishing I'm using the auto-mining script from one of the meta posts here and it doesn't works!  At first I got steady returns but the returns seem to diminish over time. Using Fiddler I confirmed that the server seems to release less and less coins.  This is unacceptable! I am a loyal customer paying nothing and I demand that my auto-mining script continues to yield returns forever!  If you cannot deliver on that please refund what I have payed for using this site.  Plz advise!    In case you didn't notice: This is a parody of over-demanding, leeching askers on Stack Overflow. Exporting Data From Salesforce - REST or SOAP? We have a requirement where we need to export records from salesforce tables into our application programmatically. I am reading on the various API's for data integration from salesforce mainly SOAP vs REST API's.  From what I understand, REST should be used when the web service requests are from mobile devices or browser based clients (since they understand JSON). Is that true? If that's the case how do Bulk REST API's fit the bill (since they are meant for bulk data transfers)?  I would like to get your thoughts on what are pros and cons in using SOAP or REST API's to export data records. Note that the requests are being made a java ee server application programmatically. After retrieving the records (probably in batches) from salesforce records we process (validate, filter etc) them and load them in our internal tables.  Thanks. Is there a way to include all the jar files within a directory in the classpath?  I'm trying java -classpath lib/*.jar:. my.package.Program and it is not able to find class files that are certainly in those jars.  Do I need to add each jar file to the classpath separately? A question here on meta for instance may stick around for quite a while. A feature-request  maybe even for months. Then the status (tags) gets changed to  or  or whatever and the OP does not get notified.  On a normal post-edit we get a notification but retagging does not count for that. Please add retagging to the edit notifications. Position of the adverb "substantially" Variation on Vandermonde's identity How can you show that $$ \binom{2n}{n}^2 = \sum_{m=0}^{n} \binom{2n}{2m} \binom{2m}m \binom{2n-2m}{n-m} $$?  I was fooling around with random walks, and apparently both expressions are supposed to be the number of unweighted random walks on a 2D square lattice of $2n$ steps that ends at the origin.  Whole thing reminds me of Vandermonde's identity but I can't it. Any hints? Equivalent statement of AC or not? Here's a corollary of AC stating that: if there exists an onto mapping $f:A\to B$, then there exists a 1-1 mapping $g:B\to A$. What I'm confused about is that whether or not  AC can be derived from this proposition, in return? I have tried but haven't found a proof. Any help would be appreciated. Understanding Join Attributes by Location in QGIS? I wonder if there is somewhere an explanation for the parameters that can be set when running the Algorithm "Join Attributes by Location" in QGIS 2.18.  I had a look here:       but there is no explanation. Any hints? How to do a generalized linear model with multiple dependent variables in R? What if I accidentally run command "chmod -R" on system directories (/, /etc, ...) How do you reset the sa password? Close locked file in Windows Share using Powershell and Openfiles I work with a lot of folder shares, but there are a bunch of locked files which have been opened by some other process.  I need to close those files. So far I've been using MMC - System Tools - Shared Folders - Open Files.  It would be far more convenient if I could use PowerShell to filter the list/table retrieved by OpenFiles.exe and once I get the file ID close it with net file  /close, or some other PS native means to similar effect.  I am new to PowerShell, so I wonder if there is a way to create a PS script that receives the file's path and then used the file ID to close that file? Determining statistical probability related to a string event of dates Starting eclipse from unity launcher How to compute $\lim\limits_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$, where $\{x\}$ is the fractional part of $x$? I've stumbled upon the following problem:  $$\lim_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$$  where "{}" notates the fractional part.  I've never studied this kind of problem, there exists any reference that I could read about this type of problem? Puzzle: Find largest rectangle (maximal rectangle problem)