I understand the theoretical part of RSA (the concept of public and private keys), but I don't understand the mathematical part. Can anyone please explain it to me in simple terms? Thanks.
What is the definition of textbook or "raw" RSA?  What are some of the properties of textbook RSA?  How does it differ from other schemes based on RSA?
Let $G$ be a finite abelian group s.t. it contains a subgroup $H_{0} \neq (e)$ which lies in every subgroup $H \neq (e) $. Prove that $G$ must be cyclic.   Also what can be said about $o(G)$ ?    I'm clueless about this problem from Herstein. I tried to think $G$ might be a solvable group and its subgroups are all normal (as $G$ is abelian) . But I'm unable to get further. Cardinality of the Irrationals Possible Duplicate:          We previously proved that $\mathbb{Q}$, the set of rational numbers, is countable and $\mathbb{R}$, the set of real numbers, is uncountable. What can you say, then, about the cardinality of the irrational numbers?  I would say that the cardinality of irrational numbers is uncountable. That would be because the set $\mathbb{Q}$ is a subset of $\mathbb{R}$. The irrationals is also a subset of $\mathbb{R}$. Basically, my thought is that the continuum is composed of irrationals and rationals (only two subsets of reals). Because we can prove that the rationals are countable by Cantor's proof, then the remaining subsets of $\mathbb{R}$, the irrationals, has to be uncountable for $\mathbb{R}$ to be uncountable. My concern is how to go about the prove this (rigorous, intro level). In Data Extension one field 'HTML' have Data that I have shown below, Now I have to Find the 'Href', and and at the last of URL append some text like '&amp;MC='. It may have Multiple 'Href'. Please help me on this.   &lt;table width="540" style="margin: 0px; padding: 0px;" bgcolor="#ffffff" border="0" cellspacing="0" cellpadding="0"&gt;  &lt;tbody&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;    &lt;h5 style="margin: 0px; padding: 0px 0px 2px; line-height: normal; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 16px; font-weight: normal;"&gt;    &lt;a style="text-decoration: none;" href="https://test.4.com/testRegistration/testLobbyServlet?target=reg20.jsp&amp;eventid=897605&amp;sessionid=1&amp;key=2F3D1EB963D9DB7738BF2877DFFDBA01&amp;partnerref=Social&amp;sourcepage=register&amp;loc=zOTlocz&amp;prod=zWAz&amp;tech=zsecz&amp;prog=zOTprogz&amp;type=zOTtypez&amp;media=zWCz&amp;country=zUSz" alias="Success with Enterprise Mobility: Making email and Office 365 secure on mobile devices"&gt;    Success with Enterprise Mobility: Making email and Office 365 secure on mobile devices     &lt;/a&gt;    &lt;/h5&gt;    &lt;p style="margin: 0px; padding: 0px; line-height: 20px; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: normal;"&gt;    &lt;span style="color: rgb(103, 103, 103);"&gt;    &lt;em&gt;December 9, 2014, 10:30 A.M.&amp;ndash;11:30 A.M. Pacific Time&lt;/em&gt;&lt;br&gt;    An enterprise mobility strategy involves identity, management, and productivity. In this session featuring Brad Anderson, you will learn about the integration and the Office mobile apps while enabling secure mobile productivity.    &lt;/span&gt;    &lt;/p&gt;    &lt;/td&gt;   &lt;/tr&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;&amp;nbsp;    &lt;/td&gt;   &lt;/tr&gt;   &lt;tr&gt;    &lt;td valign="top"&gt;    &lt;h5 style="margin: 0px; padding: 0px 0px 2px; line-height: normal; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 16px; font-weight: normal;"&gt;    &lt;a style="text-decoration: none;" href="http://test.TTr.com/?Wt.mc_id=IG15W2NWTN&amp;loc=zOTlocz&amp;prod=zWAz&amp;prod=zWSz&amp;tech=zCLz&amp;prog=zOTprogz&amp;type=zEVz&amp;media=zOTmediaz&amp;country=zUSz" alias="Test: Everything about enterprise technology under one roof"&gt;    Test: Everything about enterprise technology under one roof    &lt;/a&gt;    &lt;/h5&gt;    &lt;p style="margin: 0px; padding: 0px; line-height: 20px; font-family: &amp;quot;Segoe UI&amp;quot;, &amp;quot;Lucida Grande&amp;quot;, Verdana, Arial, Helvetica, sans-serif; font-size: 12px; font-weight: normal;"&gt;    &lt;span style="color: rgb(103, 103, 103);"&gt;    &lt;em&gt;May 4&amp;ndash;8, 2015, Chicago, IL&lt;/em&gt;&lt;br&gt;    If you&amp;rsquo;re serious about technology, you don&amp;rsquo;t want to miss Test. This event will be the intersection of everything in enterprise technology. Get ahead in your job and your career.    &lt;/span&gt;    &lt;/p&gt;    &lt;/td&gt;   &lt;/tr&gt;  &lt;/tbody&gt; &lt;/table&gt; Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle I need to evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle.    Attempt: Let $\gamma(t) = e^{it} $ where $t \in [0,2 \pi]$. How can I get rid of the absolute values in the differential? What is a simple way to create a binary relation symbol on top of another? What is a simple way to have \ll on top of \gg with equal size and vertically center aligned and have them work as a binary relation symbol like \lessgtr? The commands \underset and \overset cannot be used because they do not treat the two symbols equally, and they do not vertically center. What are FML and BWSS? I see this ad sometimes and I would like to know what the acronyms are. Expected maximum of sub-Gaussian I'm trying to answer the following question from the book :  Let $X_1,X_2,\dots$ be a sequence of sub-gaussian random variables, which are not necessarily independent. Show that   $E\bigg[ \max_i \frac{|X_i|}{\sqrt{1 + \log i}} \bigg] \le CK$,  where $K = \max_i \|X_i\|_{\psi_2}$. Deduce that for ever $N \ge 2$ we have   $E\bigg[ \max_{i \le N} |X_i| \bigg] \le CK \sqrt{\log N}$.  I've tried to figure out what is the distribution of the maximum of Gaussians, but I'm reaching only inequalities that that don't help me answer the question.   I've also seen a similar question .  Does anyone have a clue or something to start with in order to answer this question?  Thanks! Earlier today, I was suspended from chat due to an inappropriate message (I totally deserved it, but that's not the point). I looked at my phone, and this is all that it told me:    ...which confused me because chat was still moving as normal. I didn't realize that I had been suspended until I checked on my computer to see what the heck was going on.  To me, "This room is read-only" sounds like some sort of database lockup or something related specifically to the room, not the user. It doesn't give any feedback to indicate that the room will be "read-only" for 30 minutes, and doesn't mention that all other rooms are also "read-only". Even a message saying just "You have been suspended from chat" would be more helpful. Find rational points on $x^2 + y^2 = 3$ and on $x^2 + y^2 = 17$ $(a)$ Find all rational points on the circle $x^2 + y^2 = 3$, if there are any. If there is none, prove so.  $(b)$ Find all rational points on the circle $x^2 + y^2 = 17$, if there are any. If there is none, prove so.  I'm not sure how proceed with finding a general formula (if there is one)  I know that for $(a)$ there is no rational points but I don't know how to explain that there are none.   whereas for $(b)$ there are such points, $(1,4)$ for example. I think that we can find the intersection between the line $y=m(x-1)+4$ and $x^2 + y^2 = 17$  Any help is appreciated! What is the difference between correlation, causation and prediction? Suppose we have a set of events $\Omega$, containing events $A$ and $B$. My econometrics professor tried to distinguish the following three terms today.    Causation --- $A$ causes $B$ if the occurrence of $A$ always leads to another specific outcome $B$. For example, clapping my hands causes a sound to be emitted.  Prediction --- $A$ predicts $B$ if on average, $B$ is the expected outcome from $A$ occurring. In other words, whereas causality is deterministic, prediction is probabilistic. For example, studying for a test would predict doing well on the exam. But there's no guarantee.   Correlation --- $A$ and $B$ are correlated if when one occurs the other does too. But there may be some hidden variable causing both.    Are these distinctions meaningful? Or did he make these terms up?   My Questions   What is the difference between causation and correlation?  Are "causes" always deterministic? Does someone know how to set a command block with a command inside using the setblock command?  I have created this code /setblock &lt;x&gt; &lt;y&gt; &lt;z&gt; command_block {TileEntityData:{Command:"testfor @p[_=1]"}} but it doesn't works.  Do someone know how to do that? Is it completely against the Java way to create struct like objects?  class SomeData1 {     public int x;     public int y; }   I can see a class with accessors and mutators being more Java like.  class SomeData2 {     int getX();     void setX(int x);      int getY();     void setY(int y);      private int x;     private int y; }   The class from the first example is notationally convenient.  // a function in a class public int f(SomeData1 d) {     return (3 * d.x) / d.y; }   This is not as convenient.  // a function in a class public int f(SomeData2 d) {     return (3 * d.getX()) / d.getY(); } How do I verify that a string only contains letters, numbers, underscores and dashes? I know how to do this if I iterate through all of the characters in the string but I am looking for a more elegant method. Under what conditions is the exponential map on a Lie algebra injective? Let $G$ be a Lie group with Lie algebra $\mathfrak{g}$ and let $\exp :\mathfrak{g}\rightarrow G$ be the exponential map.  In his blog,  that if a Lie group is not simply-connected, then $\exp$ will not be injective.  Conversely, is it true that if a Lie group is simply-connected, then $\exp$ is injective?  If not, what is a counter-example? I have a bunch of external and internal HDDs that I use on a Linux system. I only have Linux systems, so using a Linux file-system would only make sense, right? However I'm currently using NTFS everywhere, because it gives me the most usable space out of HDDs.  I would like to switch to Linux file-systems now though, mostly because of permissions and compability (e.g. I can't get my LUKS encrypted NTFS partition to resize under Linux, keeps telling me to chkdsk under Windows).  However when I formatted those HDDs I tried out a bunch of different filesystems and every Linux filesystem, even ext2 which as far as I know has no journaling, used a lot of space for itself. I don't recall exact values, but it was over 100GB that NTFS got me more on a 2TB HDD, which is a lot.  So my question is: Is there a way to make ext-filesystems use less space for themselves? Or is there another filesystem (I've tried ext2, ext3, ext4, NTFS and vfat - None of them came even close to the usable space NTFS offered me) with perfect Linux support and great usable space?  I'd love to hear about how and why filesystems (especially ext2 which has no journaling) use that much more space than NTFS and I don't know where else to ask. I'd mostly prefer a way to use ext4 without journaling and anything else that uses up this much space, if that's possible. Can inner classes access private variables? class Outer {      class Inner {     public:         Inner() {}         void func() ;     };  private:     static const char* const MYCONST;     int var; };  void Outer::Inner::func() {     var = 1; }  const char* const Outer::MYCONST = "myconst";   This errors out when I compile with class Outer::Inner' has no member named `var' How to develop a SharePoint Designer Workflow Action for use in SharePoint (2013) online Looking for a short story about an insect-like alien captured by humans on its own planet This poor creature is taken aboard the spaceship and the humans do not know that it is intelligent.  The alien can repeat what it hears, e,g, "pass the sugar".  It is able to escape at night and it communicates messages to its fellow aliens.  It directs that they turn up the heat of the atmosphere (somehow they can do this) so as to force the humans to leave.  The alien protagonist states that it will die w/ the humans or leave with them. I'm experiencing a bug where when the machine comes back from standby a monitor connected via displayport (MST) does not come back on, however the windows are still in the area it cover if it did come on.  The only way to recover from this short of a restart is to disable and reenable the display now I can do that via the command line just fine but when the display is disabled all the windows get rearranged onto the remaining screen.  Is there a way to persist the window positions and restore them so my script could do this sequence:-   enumerate windows, store positions display off (messing up positions) display on (making the display work again, yay!)  restore position of the windows   I can do step 2 and 3 just fine but I'm lost for step 1 and 4  I know I can force a position per app but that's not what I want as I could be doing different things and have the same apps in different positions, I also have multiple terminals open, I need the current positions storing somehow and restoring.  Any help would be appreciated! Parent Field in Lightning Datatable Are Parent Fields supported in lightning Datatable?  I'm trying to display Account Name with Contact information, but it seems parent fields are not supported in lightning datatable.  Component:  &lt;aura:component controller="PagingSortingController"&gt;     &lt;aura:attribute name="mydata" type="Object"/&gt;     &lt;aura:attribute name="mycolumns" type="List"/&gt;     &lt;aura:handler name="init" value="{! this }" action="{! c.init }"/&gt;     &lt;lightning:datatable data="{! v.mydata }"          columns="{! v.mycolumns }"          keyField="con.id"         onrowselection="{! c.getSelectedName }"/&gt; &lt;/aura:component&gt;   Controller:  ({     init: function (cmp, event, helper) {     cmp.set('v.mycolumns', [                 {label: 'Contact Name', fieldName: 'Name', type: 'text'},                 {label: 'Phone', fieldName: 'Phone', type: 'phone'},                 {label: 'Email', fieldName: 'Email', type: 'email'},                 {label: 'Account Name', fieldName: 'Account.Name', type: 'text'}             ]);         helper.getData(cmp);     }  })   Helper:  ({     getData : function(cmp) {         var action = cmp.get('c.getContacts');         action.setCallback(this, $A.getCallback(function (response) {             var state = response.getState();             if (state === "SUCCESS") {                 cmp.set('v.mydata', response.getReturnValue());             } else if (state === "ERROR") {                 var errors = response.getError();                 console.error(errors);             }         }));         $A.enqueueAction(action);     } })   Apex Controller:  @AuraEnabled     public static List&lt;Contact&gt; getContacts() {         List&lt;Contact&gt; contacts =                  [SELECT Id, Name, Phone, Email,Account.Name FROM Contact];         return contacts;     }