The question “” assumes the factors are known. This got me wondering if it is possible to calculate the value of $d$ when being given only the values of $c$, $n$ and $e$… and factors remain secret.   If it’s possible, is there an easy way to do so? If it’s hard/complex, what exactly makes it hard/complex? And in case it’s generally impossible to calculate $d$ using only those values, why?   This may be an amateurish question, but I couldn’t find the answer at Crypto.SE – so, I’m asking.
When given $p = 5, q = 11, N = 55$ and $e = 17$, I'm trying to compute the RSA private key $d$.  I can calculate $\varphi(N) = 40$, but my lecturer then says to use the extended Euclidean algorithm to compute $d$. That's where I get stuck.    Here's my work so far:  First I use the Euclid algorithm to calculate:  40 = 2(17) + 6  17 = 2(6) + 5 6 = 1(5) + 1 = gcd   So I know the GCD is 1. Applying the 'extended' section of the algorithm:  6 = 40-2(17) 5 = 17-2(6) 1 = 6-1(5) 1 = 6-1(17-2(6)) 3(6) = 1 (17) 3(40 - 2(17)) - 1(17) 3(40) - 3(17)   I know the answer is $33$, but I have no idea how to get there using the extended Euclidean algorithm. I can't figure out why I'm getting $3(40) - 3(17)$ when I know the answer should contain $33$.
Converting ArcGIS layer style to Styled Layer Descriptor (SLD) file? I am putting together a GIS server using GeoServer and need some help with importing my layer styles from ArcGIS 10 to  format.    I have one layer in ArcMap properly symbolized and labeled, how can I get this layers symbolization and labeling into a SLD file? How to shrink Windows 7 boot partition with unmovable files I have just bought an HP laptop with Windows&nbsp;7 (64 bit). It has a 500&nbsp;GB HDD with three partitions: a small hidden system partition, a 12&nbsp;GiB HP recovery partition, and a 450&nbsp;GiB C: boot partition.  I would like to split this large C: partition into two partitions, leaving only 100&nbsp;GiB for the system, and giving the rest to a new data partition.  Although the Windows built-in Disk Management utility has an option to shrink the bootable partition, it only allows me to shrink it roughly by half, even though only 20&nbsp;GiB on the partition is used. As far as I understand, system unmovable files lie in the middle of the partition, preventing Disk Management utility to do what I want.    And since new HP laptops don't come with OS installation disks (they only allow you to create recovery disks yourself), I can't just repartition HDD and then reinstall OS.  So, is there a way to shrink the C: bootable partition and preserve Windows&nbsp;7 working?  P.S.: I have tried to use the third-party  utility, and after shrinking the partition, Windows&nbsp;7 stopped booting, with a . System recovery didn't work, and I had to do factory recover. Since this is a long process, I would like to avoid doing it again :) So, please, suggest only proven solutions. Pipe to multiple files in the shell I have an application which will produce a large amount of data which I do not wish to store onto the disk. The application mostly outputs data which I do not wish to use, but a set of useful information that must be split into separate files. For example, given the following output:  JUNK JUNK JUNK JUNK A 1 JUNK B 5 C 1 JUNK   I could run the application three times like so:  ./app | grep A &gt; A.out ./app | grep B &gt; B.out ./app | grep C &gt; C.out   This would get me what I want, but it would take too long. I also don't want to dump all the outputs to a single file and parse through that.  Is there any way to combine the three operations shown above in such a way that I only need to run the application once and still get three separate output files? I’m a newbie in Python. I’m learning regexes, but I need help here.  Here comes the HTML source:  &lt;a href="http://www.ptop.se" target="_blank"&gt;http://www.ptop.se&lt;/a&gt;   I’m trying to code a tool that only prints out http://ptop.se. Can you help me please? Let $D \subset \mathbb{C}$ be an open, connected set and let $\{ u_n \}$ be a sequence of harmonic functions with $u_n: D \longrightarrow (0, \infty)$. Show that if $u_n(z_0) \rightarrow 0$ for some $z_0 \in D$, then $u_n \rightarrow 0$ uniformly on compact subsets of $D$.  If you could offer a hint or a helpful question to get me started I'd appreciate it.   Progress: I now see why showing it for the unit disk suffices (any compact subset in $D$ can be covered by finitely many disks each which is contained in $D$). Convert from a specifc range to another one TexShop will not compile without trashing aux files after every error I have a couple of LaTeX files with the same problem. If I produce an error, fix it, and then try to compile a pdf, I get the following error.  )Runaway argument? {{ ! File ended while scanning use of \@newl@ablel. &lt;inserted text&gt;                 \par l.90 \begin{document}   If I then click on the console or trash my .aux file, it compiles fine. Any thoughts on what is going on and how to prevent this annoying extra step? Is a 1st-level spell cast using a 4th-level slot a 1st-level spell, or a 4th-level spell? As the title says: Is a 1st-level spell cast using a 4th-level slot a 1st-level spell, or a 4th-level spell? What is the easiest way to handle huge numbers in C? I need to store values in the Area 1000^900, or in more human readable form 10^2700. Does anybody know of an easy way to do that? Any help would really be appreciated! Cosine of the sum of two solutions of trigonometric equation $a\cos \theta + b\sin \theta = c$ Question: If $\alpha$ and $\beta$ are the solutions of $a\cos \theta + b\sin \theta = c$, then show that: $$\cos (\alpha + \beta) = \frac{a^2 - b^2}{a^2 + b^2}$$  No idea how to even approach the problem. I tried taking two equations, by substituting $\alpha$ and $\beta$ in place of $\theta$ in the equation and manipulating them, but that didn't get me anywhere. Please help! Winforms issue - Error creating window handle We are seeing this error in a Winform application.  Can anyone help on why you would see this error, and more importantly how to fix it or avoid it from happening.   System.ComponentModel.Win32Exception: Error creating window handle.    at System.Windows.Forms.NativeWindow.CreateHandle(CreateParams cp)    at System.Windows.Forms.Control.CreateHandle()    at System.Windows.Forms.Control.CreateControl(Boolean fIgnoreVisible)    at System.Windows.Forms.Control.CreateControl()    at System.Windows.Forms.Control.OnVisibleChanged(EventArgs e)    at System.Windows.Forms.ButtonBase.OnVisibleChanged(EventArgs e) $\DeclareMathOperator{\Char}{char}$$\DeclareMathOperator{\Aut}{Aut}$ Let $G$ be a finite group, $H$ a subgroup, such that $H \Char G$. If $\phi \in \Aut(H)$ is there an automorphism $\widehat{\phi} \in \Aut(G)$ such that $\widehat{\phi}|_H$ = $\phi$?  In words, if $\phi$ is an automorphism of $H$, is there necessarily an automorphism $\widehat{\phi}$ of $G$ where $\widehat{\phi}$ maps the elements in $H$ to $H$ in exactly the same way?  I am thinking this is false (consider the non-finite example of $\bar{Q}$ and $\mathbb{C}$), but would like a counter example (for the finite case). I've only been able to resolve this far  $$ d \mid n \Rightarrow \exists l \in \mathbb{Z}\; \textrm{such that} \; n=dl \Rightarrow x^{q^n} - x = x^{q^{dl}} - x.$$  I can't move forward. In Random forest algorithm, Breiman (author) constructs similarity matrix as follows:   Send all learning examples down each tree in the forest If two examples land in the same leaf increment corresponding element in similarity matrix by 1 Normalize the matrix with number of trees   He says:     The proximities between cases n and k form a matrix {prox(n,k)}. From their definition, it is easy to show that this matrix is symmetric, positive definite and bounded above by 1, with the diagonal elements equal to 1. It follows that the values 1-prox(n,k) are squared distances in a Euclidean space of dimension not greater than the number of cases.    In his implementation, he uses sqrt(1-prox), where prox is a similarity matrix, to convert it to distance matrix. I guess it has something to do with the "sqaured distances in a Euclidean space"-quoted above.  Can somebody shine a little light on why it follows that 1-prox are squared distances in a Euclidean space and why he uses squared root to get distance matrix? When to use Path in WPF Binding? How does the British-Irish Visa Scheme (BIVS) work? I am an Indian citizen and have applied for the Standard Visitor visa to the UK, and wish to travel to Ireland by using the BIVS scheme.    Do I need to fill up a separate application for BIVS endorsement or is it handed out automatically?  Also, If I enter the UK, and then travel to Ireland, can I re-enter the UK again? I'm Egyptian and flying to Cairo from Tbilisi, via Istanbul. The first flight Tbilisi-Istanbul is on Atlasjet, then from Istanbul to Cairo I am flying on Egyptair. For that, I have to recheck in at Istanbul to my Egyptair flight  Will I need to pass passport control at Istanbul airport to collect my bags and check in on Egyptair? Will I need a transit visa for that? Or it can be all done through neutral zone? How do I rename all folders and files to lowercase on Linux? I have to rename a complete folder tree recursively so that no uppercase letter appears anywhere (it's C++ source code, but that shouldn't matter).  Bonus points for ignoring CVS and Subversion version control files/folders. The preferred way would be a shell script, since a shell should be available on any Linux box.  There were some valid arguments about details of the file renaming.   I think files with the same lowercase names should be overwritten; it's the user's problem. When checked out on a case-ignoring file system, it would overwrite the first one with the latter, too. I would consider A-Z characters and transform them to a-z, everything else is just calling for problems (at least with source code). The script would be needed to run a build on a Linux system, so I think changes to CVS or Subversion version control files should be omitted. After all, it's just a scratch checkout. Maybe an "export" is more appropriate. Equicontinuity on a compact metric space turns pointwise to uniform convergence I know that   If $\{f_n\}$ is an equicontinuous sequence,  defined on a compact metric space $K$, and for all $x$, $f_n(x)\rightarrow f(x)$, then $f_n\rightarrow f$ uniformly.  I'm having trouble proving this.  I see the same problem  but am having trouble following the proof, particularly with part (3).  Can someone guide me through a proof of this result? How to preserve bookmarks when rearranging pages of a PDF file with tools like pdftk? I am using pdftk to rearrange pages of a pdf file with bookmarks/outlines, but after that, the output file lost the bookmarks of the original.   My command is pdftk in.pdf cat 1-22 43 23-42 44-end output out.pdf.  I was wondering how I could keep the bookmarks while rearranging pages?