I tried to solve this equation but without a success:  $3x^{2}+6x+1 \equiv 0 \pmod {19}$  I concluded hat $x(x+2)\equiv 6 \pmod{19}$, the only way i think to solve this is by just trying all the options. But there must be a more efficiant way.  I would like to get help with that, thanks
I need to solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$  I saw the same problem here -     but didn't understand how he got to the conclusion   $x(x+2) \equiv 6 \pmod {19}$  and anyway im trying to solve it how we learned in class -   multiply both sides and the modulo by $4a$ then solve the two equations  $y^2 \equiv b^2 -4ac \pmod {4an}$  $2ax + b \equiv y \pmod {4an}$  so I tried multiplying the hole thing by $4a$ , that is $4 \times 3$  and got to $(2 \times 3x + 6)^2 \equiv 36 -4 \times 3 \pmod {19 \times 4 \times 3}$  now I am stuck . any help will be appreciated
I want to convert .mov to .mp4! I saved the video from iMovie but it is in .mov format! How do I convert it to .mp4?  I'm using a MacBook and I want to share it to my phone, but my phone can't open .mov format video. Which is the correct use of these two words, and in which context should one be used rather than the other? Object on curve wont stay flat! Separable Hilbert space have a countable orthonormal basis I want to show that every an infinite-dimensional separable (contains countable dense set) Hilbert space has a countable orthonormal basis.  I know that every orthogonal set in a separable Hilbert space is countable, it is help me with the proof? How to yield from parallel tasks in .NET 4.5 I'm using 3d to speed up production of 2d graphics of machines and structures (which have a lot of straight lines, objects and little details repeated all over the place).  The goal is to have an isometric background image that repeats seamless. I set the camera with orthographic projection and 45° of rotation.    And manually cut the vertical borders in an image editor in the position where it repeats. Then I can do something like this:    Instead of cutting it manually every time I do a test, I would like to set the camera view position and height from Blender. Then I can render an already seamless repeated image.  Those two Empty objects in the boundaries are where the camera borders should be. However I have no clue how to accurately set up the camera in this case. How can I do this? Find $P(12)$ when $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$ let $P(x)$ be a polynomial of degree $11$ such that  $P(x)={1\over(x+1)}$, for $x=0,1,2,......11$  then find value of $P(12)$ I want to assign the result of an expression (i.e., the output from a command) to a variable and then manipulate it – for example, concatenate it with a string, then echo it.  Here's what I've got: #!/bin/bash cd ~/Desktop; thefile= ls -t -U | grep -m 1 &quot;Screen Shot&quot;; echo &quot;Most recent screenshot is: &quot;$thefile;  But that outputs: Screen Shot 2011-07-03 at 1.55.43 PM.png Most recent screenshot is:   So, it looks like that isn't getting assigned to $thefile, and is being printed as it's executed. What am I missing? How do I boot into recovery mode? What alternative notation of subscripts/superscripts that are also treated as SYMBOLS in Mathematica? With the new permission model for Marketing Cloud Installed Packages, there is a problem with the "Read"-Scope for Data Extensions.  If an installed package is granted the permission/scope "Data Extensions - Read" the API-Call fails with HTTP 403 "Forbidden".  How to provide read access to Data Extensions?  Related documentation: Assigning variables with dynamic names in Java The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition Why do the planets' orbital distances fall on an exponential curve? Background: I was recently reading a book on the planets to my son and I noticed a pattern in the distributions of the planets.  The planets' distances roughly follow an exponential distribution.  Below is a plot of scaled, log orbital distances $$ \tilde{d_n} = \frac{\log(d_n/d_1)}{\log(d_2/d_1)} $$ with the line $an+b$:   Where $d_1$ corresponds to Mercury and so on. Ceres is included, Pluto is excluded.  By linear regression, $a = 0.90, b = -1.06$.  For the statistically minded, the data has a Pearson's correlation of 0.996.  Note that this is a well known phenomenon, see  and references.  The code used to generate the plot may be provided on request.  Question: What is the mechanism that leads to this distribution?  Aside: Is there a good introductory text on solar system formation for the mathematically inclined?  Update: This is also known as Titius–Bode law. My question relates to Chapter 3, Exercise 8 in &quot;Baby Rudin&quot;. It states: If $\sum_n a_n$ converges, and if $\{b_n\}$ is monotonic and bounded, prove that $\sum_n a_n b_n$ converges. My attempt would have been: Since $\{b_n\}$ is monotonic and bounded, $\{b_n\}$ converges and it exists $\inf \{b_n\}$ as well as $\sup \{b_n\}$. But then we have $$ \left| \sum_n a_n \inf \{b_n\} \right| \leq \left| \sum_n a_n b_n \right| \leq  \left| \sum_n a_n \sup \{b_n\} \right| \leq \max \left( \left| \sup \{b_n\} \right|, \left| \inf \{b_n \} \right| \right)\varepsilon \leq \tilde{\varepsilon} $$ since $\sum_n a_n$ converges and $\max \left( \left| \sup \{b_n\} \right|, \left| \inf \{b_n \} \right| \right)$ is a finite number. This would imply, by the comparison test, that $\sum_n a_n b_n$ converges as well. $\quad \Box$ But as there was a way longer, more rigorous proof chosen in this , I'm a bit suspicious that my proof is not complete. Am I missing something?  EDIT: Thanks everyone! @hermes: The last part of your proof gave me the following idea. As $\lim_{n \to \infty} b_n = c$ and $\{b_n\}$ is monotonic, couldn't we just set $b_n = c - c_n$ with a monotonically decreasing sequence $\{c_n\}$ which has $\lim_{n \to \infty} c_n = 0$. Then we have $$\sum_n a_n b_n = \underbrace{c \sum_n a_n}_{\text{converges by assumption}} - \underbrace{\sum_n a_n c_n}_{\text{converges by Theorem 3.42}} \leq \varepsilon_1 - \varepsilon_2 = \varepsilon $$ since  Theorem 3.42 Suppose  the partial sums of $\sum_n a_n$ form a bounded space $\quad \checkmark$ $c_0 \geq c_1 \geq c_2 \geq \dots \quad \checkmark$ $\lim_{n \to \infty} c_n = 0 \quad \checkmark$  Then $\sum_n a_n c_n$ converges.  Thus $\sum_n a_n b_n$ converges as well. $\quad \Box$ Now that should hold, I think. So I wouldn't need to go through all the estimates. Link2SD not working completely My Link2SD doesn't seem to be fully working. I noticed this when updating the Facebook application. Google Play prompted me of insufficient storage. I first uninstalled some apps but I got curious so I checked Link2SD's storage info, I got this:   (Click image to enlarge)  As you can see, the internal storage only has mere 70mb left. What's peculiar is, these are the only apps I have NOT linked:   (Click image to enlarge)  I tried moving one linked app (Amazing Alex) to the sd card (normal Android way) and sure enough, the free space on my internal storage got bigger by about an additional 20mb-ish.  Why is this happening? Why isn't Link2SD moving the data to my sdext2? How do I solve it? Cyclic orbit animation I'm trying to make one object orbit another. But I want it to repeat, rather than stop at 100 frames. It seems there is no option for this. Is there a way to make this happen? 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; Is there a word to describe the virtue of "to do something and ask for nothing in return"? I am wondering if there is a positive, formal counterpart to the slang "No strings attached" to describe, for example, a parent's unquestioned devotion to their children, or the virtue of someone's "a friend in need is a friend in deed", help first, question later mentality. What is the difference between [0-9]+ and [0-9]++?