I can find lots of examples for $ax + by = c$, but how do I get started with the $\text{^2}$ there?  My specific equation is; $2x^2 - 154y = 116$  I thought I would reduce and substitute to get a familiar form; $s - 77t = 58$  which I realized has a trivial solution; $(s_0,t_0) = (58,0)$  I'm not particularly sure where to go from here, or even if this is the right path to take.
I understand what the Chinese remainder theorem is. However I am not sure how to apply it to my question. Can someone explain please?
SEO regarding using separate  tags for the logo and website name Is is true &lt;h1&gt; tag should not have more than 1 on every page for SEO?   Every pages on the header, it includes and &lt;h1&gt; tag. Website Name which show an image from logo class, like this:  &lt;div id="header"&gt;   &lt;h1 class="logo"&gt;      &lt;a href="#"&gt;Website Name&lt;/a&gt;   &lt;/h1&gt; &lt;/div&gt;   and I also include &lt;h1&gt; on the contact page, help, etc and article page for example:  &lt;h1&gt;Contact Us&lt;/h1&gt; &lt;h1&gt;Name of the Article Title here&lt;/h1&gt;   On the homepage, it just has one &lt;h1&gt; for the logo Site Name... other pages have 2 &lt;h1&gt; tags In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? Present perfect for past action with present effect What did my neural network just learn? What features does it care about and why? I think this was more of a fantasy series, though it was more subtle than The Lord of the Rings IIRC. Set in modern times - though there was some alternate realm thing that was less modern I think.   I read it about ten years ago, I think, and there were a number of books at that time. My brother and I stopped reading it shortly after the main character summoned a small demon somehow who was a bad influence... I think.  It involved a boy who somehow was at some kind of training school/academy. Unsure where it was located, but it needed a classic portal to get to it I think. I clearly remember some scene involving a car driving at specific speeds to get past some barriers. There may have been something about how the school was (slowly) moving or the wards were shrinking... unsure. I don't think it was only magic based, but that was some element of it. The boy had some kind of strange power that made him an incredible fighter, but he wasn't sure how (at least from what I remember). The recordings of him training just showed a white flash I think. I remember some scene in an elevator going down to the training floor where he went to a level below some adult with him.  There was something else about him joining a group that had twelve members, one for each month, whose powers grew and lessened based on how close the date was to "their" month.  Oh, and there was something about him looking for his mother I think? Perhaps in another "realm"?   Any help is appreciated! Practical Uses for the "Curiously Recurring Template Pattern" What are some practical uses for the ""?  The "" example commonly shown just isn't a convincing example to me. Possible Duplicate:          Consider the field extension $\mathbb{Q}(\sqrt2)$. I want to show that $\sqrt5 \notin \mathbb{Q}(\sqrt2)$. If this were not the case, then we could write $\sqrt5 = a + b\sqrt2$ for $a,b\in\mathbb{Q}$. However, I do not see the contradiction here. Is there a better/easier way to prove this? Disable password access through SSH? I'm setting up a server for backing up my desktop box remotely. I want to prevent remote password access to the server, permitting only users with private keys (AKA my desktop box) to access it. How can I block remote password access while allowing physical password access to the server? Why do some Jedi disappear when they die while others don't? Some Jedi disappear when they die:   In Star Wars Episode IV: A New Hope       At the end of his duel with Vader on the first Death Star, Obi-Wan Kenobi let down his guard and concentrated for a moment, disappearing entirely just as Vader's lightsaber passed through his empty robe.   In Star Wars Episode VI: Return of the Jedi      When Luke returned to Dagobah in the Return of the Jedi, Yoda also disappears when he peacefully dies.  In Star Wars Episode VIII: The Last Jedi      When Luke is exhausted after “being” on Crait he looks into the Horizon and disappears.    And others don't:   Star Wars Episode I: The Phantom Menace      When Qui-Gon Jinn's dies after his duel with Darth Maul, he doesn't  disappear and is cremated.  Star Wars Episode VI: Return of the Jedi      When Vader/Anakin Skywalker dies on the second Death Star, he does not disappear and he is cremated by Luke.      Also, they all became a "ghost" after their death. Connect Tikz nodes via two parallel arrows I am just starting to learn using Tikz and am a little lost within its seemingly infinite amount of options and possibilities.  What I am trying to do is visualize a few Matlab function interaction (which one calls which one, what is the in- and output). Since there are only about six subroutines, I place each one manually as a node. This is an example:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{shapes,positioning}  \begin{document}  \begin{tikzpicture}[auto] \node           [rounded rectangle,draw]        (node1)     {Node 1}; \coordinate [above=of node1]                                (input); \node           [rounded rectangle,draw]    at  (-10:6cm) (node2)       {Node 2}; \draw           [-&gt;,very thick]             ([xshift=0.1cm]  input.south)  --                  node {right}                ([xshift=0.1cm]  node1.north); \draw           [-&gt;,very thick]             ([xshift=-0.1cm] node1.north) --                  node {left}                 ([xshift=-0.1cm] input.south); \draw                                            (node1) -- (node2);  \end{tikzpicture}  \end{document}     Now I would like to apply these double in/out arrows I (probably pretty awkwardly) created using xshift to all node connections, so in this example also for the connection between Node 1 and Node 2. Ideally, the space between these two arrows would be the same, independant of their angle and they would nicely connect to the outer line of the nodes. Any idea how I could achieve this? Similar questions I have found only used rectangle and orthogonal lines. In normal line integration, from what I understand, you are measuring the area underneath $f(x,y)$ along a curve in the $x\text{-}y$ plane from point $a$ to point $b$.  But what is being measured with complex line integration, when you go from a point $z_1$ to a point $z_2$ in the complex plane?  With regular line integration I can see $f(x,y)$ maps $(x,y)$ to a point on the $z$ axis directly above above/below $(x,y)$.  But in the complex case, when you map from the domain $Z$ to the image $W$, you are mapping from $\mathbb{R^2}$ to $\mathbb{R^2}$ ...it is not mapping a point to 'directly above/below'...so I don't have any intuition of what is happening with complex line integration. Finding the number of analytic functions which vanish only on a given set. Let $S = \{0\}\cup \{\frac{1}{4n+7} : n =1,2\ldots\}$. How to find the number of analytic functions which vanish only on $S$?  Options are   a: $\infty$  b: $0$  c: $1$  d: $2$ $TT^*=T^2$, show that $T$ is self-adjoint Let $V$ be an inner product space, finitely generated over $\mathbb{C}$, $T\in \operatorname{End}(V)$ that satisfies $TT^*=T^2$, show that $T$ is self-adjoint.    I know that $TT^*$ is positive so has positive square-root, thus the square root is positive definite. But I don't feel like this is a proof. Can anyone prove it without considering square root? How to calculate the Fourier transform of a Gaussian function? I would like to work out the Fourier transform of the Gaussian function   $$f(x) = \exp \left(-n^2(x-m)^2 \right)$$  It seems likely that I will need to use differentiation and the shift rule at some point, but I can't seem to get the calculation to work. Does anyone have any advice?  By the way, I am using   $$\mbox{FT}(f)(k)=\int_{-\infty}^\infty f(x)e^{-ikx}\,\mathrm d x$$  as my definition of a Fourier transform. Many thanks. What does "javascript:void(0)" mean? The generating function for the Fibonacci numbers Can the Flash run faster than light? Is there a phrase that means sleeping with someone without sex? Why does the Euclidean algorithm work for polynomials? What is the proof? Suppose I know that I can find the $\gcd$ of two integers with the Euclidean algorithm. What is the 'extension' so I can use this method also for polynomials?  Edit: I found an easy answer with less rigor which is approachable without knowledge of matrices:    also the first 3 subchapters of Seeking podcasts related to geospatial technologies?