I have the equation de ( mod x ) = 1 I currently have the values for e and x. Is there a way that I can get the value for d? I tried doing (x + e) + 1 but when I insert it into the equation, I get an answer that isn't 1.
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?
Move incoming Outlook emails to folder containing previous conversation I file email conversations in various folders. But every new email in that conversation goes to inbox, so I have to manually move it to the folder that contains the rest of the conversation. Is there a way for Outlook to do this automatically with all new emails?  What I want: Outlook will do the following automatically as long as it's running:   For all unread emails in inbox... ...if email is not the first in the conversation, search for folders where that conversation is stored. If found, move the new unread email to the first* folder it finds (except for Inbox, Trash, or Sent). Optionally: If there is more than one folder containing messages in the same conversation, then do nothing.   **If there is more than one folder containing messages in the same conversation, then do nothing*. (This extra rule is not necessary if it complicates the solution too much)  Thanks! Prove universal morphism is unique up to unique isomorphism. I'm following along Wikipedia page() on universal property, and this seems it should be trivial, but I couldn't finish the proof.  The definition I am working with:   The problem   So I want to prove that if $(A, u)$ and $(A', u')$ are universal morphism from $X$ to $F$, then there exists unique isomorphism $k: A \rightarrow A'$ such that $u' = F(k) \circ u$.   My attempt:   For any $B \in C$ and $f: X \rightarrow F(B)$, there exists unique $h: A \rightarrow B$ such that $f = h \circ u$.  Letting $B = A'$ and $f = u'$, we see that there exists unique $k: A \rightarrow A'$ such that $Fk \circ u = u'$.  This shows existence and uniqueness. We only need that $k$ is isomorphism, but this is the part I cannot prove.   Similarly, there exists unique $k': A' \rightarrow A$ such that $Fk' \circ u' = u$.  Plugging into each equation, we get  $$Fk \circ Fk' \circ u' = F(k \circ k') \circ u' = u'$$  $$Fk' \circ Fk \circ u = F(k' \circ k) \circ u = u$$  but this of course doesn't imply $F(k \circ k') = id$, so it seems useless.   Thanks for your help! If I see an answer that involves some illegal activity, such as breaking license agreements, should I then mark this as Offensive or should I simply down-vote it? Pattern matching with LIKE, SIMILAR TO or regular expressions in PostgreSQL I had to write a simple query where I go looking for people's name that start with a B or a D :   SELECT s.name  FROM spelers s  WHERE s.name LIKE 'B%' OR s.name LIKE 'D%' ORDER BY 1   I was wondering if there is a way to rewrite this to become more performant. So I can avoid or and / or like? It's my understanding that "easily" is the regular adverb for "easy", e.g. "He makes friends easily".  But in some collocations one still uses "easy", e.g. "Take it easy", "Rest easy" or "Slow down easy". Is there any rule when "easy" would be used over "easily", or does one just have to know these collocations? How can I make a div not larger than its contents? I have a layout similar to:  &lt;div&gt;     &lt;table&gt;     &lt;/table&gt; &lt;/div&gt;   I would like for the div to only expand to as wide as my table becomes. Uncheck checkboxes by changing particular checkbox state I have custom fields in contacts form named checkbox1__c, checkbox11__c, checkbox12__c, checkbox13__c.  When I check checkbox1__c then I want checkbox11__c,  checkbox12__c,  checkbox13__c to be unchecked.  When I unchecked checkbox1__c then I want checkbox11__c, checkbox12__c, checkbox13__c to be checked.  Is there any way to do this by using validation-rules? If not no way to this by validation-rules, then what is the best way to do this? .NET OpenSource projects and strong named assemblies? Explaining Horizontal Shifting and Scaling Changing permissions on serial port I'm using the Arduino IDE in Ubuntu, and am having issues with the serial port. It has worked in the past, but for reasons that may be unnecesary, I felt the need to change the ownership of some of the files from root ownership to my users ownership.  This made the IDE work correctly, but I lost the ability to use the correct serial port.  In the dev folder, the port I need is listed as permission 166. Someone (who is no longer in the area to help me) swapped the permissions to 666, which made it all work gloriously.  However, it reverted back as soon as I restarted my computer, and if I now try to use the command:  sudo chmod 666 ttyACM0   nothing happens. No error messages, but no permission change either.    How can I change it, and how can I get it to change permanently.  I apologize if this question is overly simplistic or unclear, I'm an ubuntu noob, and I wouldn't begrudge feedback! Format a date in XML via XSLT From time to time I lose all edits because of undo in Object Mode. If I enter immediately after Undo in Edit Mode I can't redo, and switching again in Object results in losing all edit history.  How can I resolve this? Separating undo history by mode or linear/unified will both be acceptable.  Edit:I think the most preferable solution will be to disable/skip edit undos when in object mode through an addon. Can Git hook scripts be managed along with the repository? We'd like to make a few basic hook scripts that we can all share -- for things like pre-formatting commit messages.  Git has hook scripts for that that are normally stored under &lt;project&gt;/.git/hooks/.  However, those scripts are not propagated when people do a clone and they are not version controlled.    Is there a good way to help everyone get the right hook scripts?  Can I just make those hook scripts point to version controlled scripts in my repo? Logo Pack - What should I include? What files should i put in a logo pack to give to clients? Should I put small, medium and large version of my logo as well as the vector file. What is a good book to study linear algebra? I'm looking for a book to learn Algebra. The programme is the following. The units marked with a $\star$ are the ones I'm most interested in (in the sense I know nothing about) and those with a $\circ$ are those which I'm mildly comfortable with. The ones that aren't marked shouldn't be of importance. Any important topic inside a unite will be boldfaced.  U1: Vector Algebra. Points in the $n$-dimensional space. Vectors. Scalar product. Norm. Lines and planes. Vectorial product.  $\circ$ U2: Vector Spaces. Definition. Subspaces. Linear independence. Linear combination. Generating systems. Basis. Dimesion. Sum and intersection of subspaces. Direct sum. Spaces with inner products.  $\circ$  U3: Matrices and determinants. Matrix Spaces. Sum and product of matrices. Linear ecuations. Gauss-Jordan elimination. Range. Roché Frobenius Theorem. Determinants. Properties. Determinant of a product. Determinants and inverses.  $\star$ U4: Linear transformations. Definition. Nucleus and image. Monomorphisms, epimorphisms and isomorphisms. Composition of linear transformations. Inverse linear tranforms.  U5: Complex numbers and polynomials. Complex numbers. Operations. Binomial and trigonometric form. De Möivre's Theorem.  Solving equations. Polynomials. Degree. Operations. Roots. Remainder theorem. Factorial decomposition. FTA. Lagrange interpolation.  $\star$ U6: Linear transformations and matrices. Matrix of a linear transformation. Matrix of the composition. Matrix of the inverse. Base changes.   $\star$ U7: Eigen values and eigen vectors Eigen values and eigen vectors. Characteristc polynomial. Aplications. Invariant subspaces. Diagonalization.   To let you know, I own a copy of Apostol's Calculus $\mathrm I $ which has some of those topics, precisely:   Linear Spaces Linear Transformations and Matrices.   I also have a copy of Apostol's second book of Calc $\mathrm II$which continues with   Determinants Eigenvalues and eigenvectors Eigenvalues of operators in Euclidean spaces.   I was reccommended Linear Algebra by Armando Rojo and have Linear Algebra by , which seems quite a good text.   What do you reccomend? '+' and 's' in permission strings If the ls -l command gives me a permission string like  rwsr-s--x   What does the 's' mean? The only sources I found mention that it can be present sometimes but do not elaborate.  What does a '+' instead of a '-' mean? I have found mentions of 'extended permission' but nothing clear. When I run sudo, what exactly happens to my environment?  When I run sudo command, it doesn't seem to see my or root's environment. For example, my path for both includes /usr/local/bin, but if I try to run one of the program's without the full path, it fails.  I thought sudo ran as root, and hence got root`s environment. Is there a different way that bash executes under sudo than under root or my normal user?  EDIT:  I have been using sudo -i lately, but recently it has been causing problems because my current working directory gets set to /root. This is as expected (sorta), but I still don't understand why sudo isn't recognizing my executables in /usr/local/bin.  EDIT:  I am running Fedora 15. What temperature should I set my water heater to? Difference between I and Me I am quite confused with the usage of I and me, Can anybody tell me what should be used in the following sentence: Your husband doesn't believe that You're older than (I / Me). Hyperref "enquotes" metadata EDIT: As Bill B. and Caramdir point out in their comments after Bill B. produced his results posted below, more information is needed in order to make a better call. To remedy, my output was produced using MiKTeX 2.8 pdflatex with no special command line flags or switches. My pdf viewer is Adobe Acrobat Pro 9.0. The platform is Windows 7. All software including hyperref is fully up to date against the latest rev levels and patches.  As I'm guessing that this is a pretty normal setup, at least in the Windows world, I'd be very interested (and grateful) in learning whether this problem affects other people or whether it's just some kind of rather weird one-off. My gut feel after seeing Bill B's results (and also after having traversed hyperref's code) is that the culprit is Adobe Acrobat or possibly MiKTeX pdflatex.    Can anyone corroborate? I'd be very grateful to know.    Original question:  I have a problem with hyperref; it "enquotes" Author and Keywords (but not Title or Subject) metadata if the data sent to these contain a comma or semi-colon (but not, say, a full stop or a colon).    I've included some figures and code that show this below.         \documentclass{article}  \newcommand*\metadata{% % uncomment all but one line below %  a  b  c%     &lt;-- no problem    a, b, c%     &lt;-- problem %  a; b; c%     &lt;-- problem %  a: b: c%     &lt;-- no problem %  a* b* c%     &lt;-- no problem }  \usepackage[   pdftitle={\metadata},    % never enquoted   pdfauthor={\metadata},   % enquoted if , or ; is present   pdfsubject={\metadata},  % never enquoted   pdfkeywords={\metadata}, % enquoted if , or ; is present ]{hyperref}  \begin{document}   Press ctl-d (in Acrobat Reader) to see pdf file metadata. \end{document}   Not only is this quite ugly but, more importantly, it interferes with metadata extracting programs used by certain document repositories.   I've worked my way through hyperref's code without much success. Would anyone have a solution for this problem?  Or advice about what I might be doing wrong?