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Isn't finding the inverse of $a$, that is, $a'$ in $aa'\equiv1\pmod{m}$ equivalent to solving the diophantine equation $aa'-mb=1$, where the unknowns are $a'$ and $b$? I have seem some answers on this site (where the extended Euclidean Algorithm is mentioned mainly) as well as looked up some books but there is no mention of this. Am I going wrong somewhere or is this a correct method of finding modular inverses? Also can't we find the Bézout's coefficients by solving the corresponding diophantine equation instead of using the extended Euclidean Algorithm? Downloading US Census data? In wikipedia FKT algorithm is given for planar graphs. Not anything for complete graphs. I need to find the number of perfect matchings in complete graph of six vertices. How to restrict some websites in Ubuntu 14.04 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. I am currently running a Dungeons and Dragons 4 campaign for a group of 9 players.  Whittling the group down to a more manageable size is not really an option since they are all family.  When we do combat it takes forever even if I have one player help me and allow them to go 2 at a time.  When we do story based adventure there are 2-3 players that do most of the talking and the others twiddle their thumbs.  I've tried encounters with many foes, encounters with only a few tough foes, dialog only encounters, social puzzle encounters, everything I can think of.  What else can I try to get this group more engaged? Why do most C programmers name variables like this:  int *myVariable;   rather than like this:  int* myVariable;   Both are valid. It seems to me that the asterisk is a part of the type, not a part of the variable name. Can anyone explain this logic? It seems to me that the terms "Teaching Assistant" and "Instructor" refer to a variety of positions. At some places, a teaching assistant is responsible for things like helping the actual lecturer by handing out papers, grading homework, etc., and instructors hold recitation sessions.  At other places, I saw the term "instructor" referring to the lecturer giving the course, while a teaching assistant is the person doing anything else (recitations, grading etc.).  Is there some widely accepted definition of the two positions?  For context: The question arose because I wasn't sure whether I'm using the correct terms in my CV -- I am a math graduate student, and I would like to make a distinction between jobs in which I only graded course assignments/final exams, and courses in which I held recitation classes* (and also participated in grading the final exams). Is it OK to use "Instructor" for the latter? What should the former be referred to as?  *In the course I'm currently teaching, the recitations are planned and written by the ones giving them (without the professors' supervision). Also, the people giving the recitations are not necessarily grad students (some already hold a PhD). I'm elaborating on that because from what I've seen, some of it could be relevant for the definition of the job. Let $M$ be an A-module and $f \in \text{End}(M)$ an idempotent endomorphism. Show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$. I don't know how to approach this exercise, using only properties of modules and direct sums, without projections. Can you help me? Thanks in advance. How can I rank observations in-group faster? Getting started with neural networks for forecasting Suppose that $f$ is continous on $[0,1]$ , differentiable on $(0,1)$ , and $f(0)=0$ and  $f(1)=1$.For every integer $n$ show  that there must exist $n$ distinct points $\alpha_1,\alpha_2\cdots,\alpha_n$ in that interval so that    $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $   Is it theorem or i can show it with basic differentiation knowledge .Please give me hint . Elevated Priviliges for Startup Applications in Windows? Is there any way to configure application that requires administrator privilages (elevation) so it's automatically started with elevated privileges and does not request elevation on every startup?  For example, I have Riva Tuner that always starts with Windows. And it always asks for elevation via UAC. I need Riva Tuner to silently start with elevated privileges and without any message from user account control (without disabling it). I replaced a non-protected receptacle with a GFCI type and now my circuit tester trips the GFCI as soon as it is plugged in.  The receptacle tested fine before replacement, ground, neutral, hot, etc.  I've double checked the hot/neutral/ground connections.  I've also tried it with the downstream load disconnected.   The GFCI trips the moment I plug in my circuit tester (before pushing the test button).  Otherwise things check out OK.  I can plug in a power tool without it tripping.  Also, the integrated test/reset button work correctly.   I've read that the integrated test button is the only one that truly matters. Is this correct or should I be concerned? I'm sure a home inspector will red flag this if their tester has the same result.  Update  My tester is by "Commercial Electric".  The tester is one of the palm sized three prong type with three leds to indicate the condition of the circuit and a button on top to test GFCI. It's new from the local box store. Use a specific forwarded key from SSH-agent? Let's say I have a key for Github, along with other keys. I've added lots of keys to my ssh agent (ssh-add -L returns lots of lines) at my home computer A. In my .ssh/config I have set up which key to use with which host, so e.g.  ssh -T -vvv git@github.com 2&gt;&amp;1 | grep Offering   gives  debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.github   Only one key is offered, as expected. But then ssh-ing to some host B with ForwardAgent yes and repeating the same command, I get  debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.linode2 debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.helium debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.github   meaning it tries all my keys. This is problematic since only a limited number of keys can be tried before servers return Too many authentication failures. So I tried editing .ssh/config on host B to include  Host github.com   IdentityFile /Users/doxna/.ssh/id_rsa.github   IdentitiesOnly yes   but then I get no key offerings, but rather  debug2: key: /Users/doxna/.ssh/id_rsa.github ((nil))   which I guess means that the key was not found(?) And after all, the key is located at my home computer A, not host B, so the question is how to refer to it at host B? Hope I managed to explain the question. Looping through files with spaces in the names? I wrote the following script to diff the outputs of two directores with all the same files in them as such:  #!/bin/bash  for file in `find . -name "*.csv"`   do      echo "file = $file";      diff $file /some/other/path/$file;      read char; done   I know there are other ways to achieve this.  Curiously though, this script fails when the files have spaces in them.  How can I deal with this?  Example output of find:  ./zQuery - abc - Do Not Prompt for Date.csv Searching for questions that have ONLY a given tag (i.e. add a range operator for tags) Checking if a double (or float) is NaN in C++ How many connected graphs over V vertices and E edges? Is there a way to calculate the number of simple connected graphs possible over given edges and vertices?   Eg: 3 vertices and 2 edges will have 3 connected graphs But 3 vertices and 3 edges will have 1 connected graph  Then 4 edges and 3 will have 4 connected graphs  Till such values...it is easy to see its  V choose E  But what about when the number of vertices are less than number of edges...how to calculate then?  I am not able to visualize that  Can it be a variation of the Stars and Bars problem  Like...number of ways 7 edges(balls) can be connected to (kept in) 5 vertices(bags) such that no vertex(bag) is isolated (is empty)  Here maybe we might have to consider the number of edges twice as each edge needs two vertices... In the Tiny Tina DLC "The Beard Makes the Man" quest, the objectives are (1) Crush five drunk dwarves, (2) Pick up five beards, and (3) Get five dwarves drunk. (The last one's optional.) I found the miner dwarves in the mine on the minimap, but they won't follow me into the crusher machine. How do I lure them? Does it have to do with getting them drunk, and how can I do that with no alcohol around? I thought getting drunk was optional?