Can anyone provide the logic why it is returning true?
Is floating point math broken?
The equation $y^2 = x^3 + k$ for $k = (4n-1)^3 - 4m^2$, with $m, n \in \mathbb{N}$ and no prime number that p is congruent to 1 modulo 4 divids m, doesn't have any answer and its proof can be obtained by using quadratic reciprocity law.  Do you know answers of this equation for two or three different values of $k$? In addition, do you know any reference about that? Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular. I'm trying to prove that statement: Prove that $\lambda = 0$ is an eigenvalue if and only if $A$ is singular.  I'm not sure if my proof is totally correct:  Suppose that $\lambda = 0$ if det(A) = $\lambda_1 \cdot \lambda_2 . . .\lambda_n = 0$ then A is singular.  If anyone could show me a better proof that would help. Why is "Nature" usually spelt with an initial capital letter in scientific journals? I am mainly referring to life science here, in case this matters.  I am not talking about the obvious cases, like capitalisation in titles, at the beginning of a sentence, etc., but when it appears mid-sentence, where one would normally expect it to be lowercase.  I've heard some explanation that it gives the impression of Nature as a goddess (see comments on this post ) - but this is probably the last thing I would have expected in a scientific article... Best books for mathematical background? Can't kill a sleeping process Does this need a comma? How to avoid nested With[]? I am trying to retrieve list items using date range based on date column. It implicit both 'Fromdate' and 'Todate'.My CAML query is also querying on two other conditions as well. I am using the below query but it is not retrieving the data.when I remove the date range from query data is retrieved fine. But i want date range as well in my query how would i do this. Little help would work for me.   camlQuery.set_viewXml('&lt;View&gt;&lt;Query&gt;&lt;Where&gt;&lt;And&gt;&lt;And&gt;&lt;Neq&gt;&lt;FieldRef Name="ID" /&gt;&lt;Value Type="Number"&gt;0&lt;/Value&gt;&lt;/Neq&gt;&lt;Eq&gt;&lt;FieldRef Name="_ModerationStatus" /&gt;&lt;Value Type="ModStat"&gt;0&lt;/Value&gt;&lt;/Eq&gt;&lt;Geq&gt;&lt;FieldRef Name="Created" /&gt;&lt;Value Type="DateTime"&gt;' + fromDate + '&lt;/Value&gt;&lt;/Geq&gt;&lt;Leq&gt;&lt;FieldRef Name="Created" /&gt;&lt;Value Type="DateTime"&gt;' + toDate + '&lt;/Value&gt;&lt;/Leq&gt;&lt;/And&gt;&lt;/And&gt;&lt;/Where&gt;&lt;OrderBy&gt;&lt;FieldRef Name="_ModerationStatus" Ascending="True" /&gt;&lt;/OrderBy&gt;&lt;/Query&gt;&lt;/View&gt;'); QGIS Align Rasters how to retain pixel values? I am attempting to align and then merge a number of rasters of the same resolution and extent, but where the pixels are slightly misaligned (creating small gaps when merged). This works fine using the Align Rasters tool, except that the pixel values are not retained and instead given a value of something like -3.23879e+8. I mostly want to keep the nodata pixels. Is this possible? Is fractional scaling ( ) available in 18.04 LTS yet? I am waiting until this is available before I install. When I run LaTeX file its gives error as  "! Package minted Error: You must have pygmentize installed to use this package", you must have pygments installed. when I go through minted documentation minted itself required pygments, so Tex friend How do I install this pygment, I don't know the procedure to install. Please guid me or any link pygement.exe file Each time I changed and saved .config/user-dirs.dirs, and after restarted the system, the XDG_DOWNLOAD_DIR are reverted:  diff --git a/.config/user-dirs.dirs b/.config/user-dirs.dirs index 8f6e2db..dcff34e 100644 --- a/.config/user-dirs.dirs +++ b/.config/user-dirs.dirs @@ -7,11 +7,9 @@  #   XDG_PUBLICSHARE_DIR="$HOME/public"  XDG_TEMPLATES_DIR="$HOME/public/template" -  XDG_DESKTOP_DIR="$HOME/private/desktop"  XDG_DOCUMENTS_DIR="$HOME/private/doc"  XDG_PICTURES_DIR="$HOME/private/picture"  XDG_MUSIC_DIR="$HOME/private/music"  XDG_VIDEOS_DIR="$HOME/private/video" - -XDG_DOWNLOAD_DIR="$HOME/var/downloads" +XDG_DOWNLOAD_DIR="$HOME/"   How to make my changes permanent? When to use self references or composition? Anvil, extra lines thingies Virtualbox Kernel driver not installed Is there a way to forget node names between TikZ pictures? I have a document with several TikZ pictures in it.  I generally use simple names for the nodes such as:  \node (A) at .....  \node (B) at .....   and so forth.  Because of this I have name clashes between the various pictures.  That's generally not a problem.  However I find myself in a position where I may or may not have defined a certain node within a given picture.  So I use the following snippet to test whether the node has been defined:  \makeatletter \long\def\ifnodedefined#1#2#3{%%   \@ifundefined{pgf@sh@ns@#1}{#3}{#2}} \makeatother   Unfortunately this fails if I've already created a node by the same name in another picture.  Is there a way to scope the definitions of nodes or is there a way to undefine nodes once you no longer need them?  P.S.  I'm aware that I could embed each picture in a standalone file and import it using \includegraphics.  Unfortunately, this approach will not work for the document I'm creating.  MWE  \documentclass{article} \usepackage{tikz} \usetikzlibrary{calc}  \makeatletter \long\def\ifnodedefined#1#2#3{%%   \@ifundefined{pgf@sh@ns@#1}{#3}{#2}} \makeatother  \setlength{\parindent}{0pt} \pagestyle{empty} \begin{document}   There's no node \textbf{D} here, so I draw a triangle:\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1); %  \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}     There is a node \textbf{D} here, so I draw a square:\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1);   \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}      There isn't supposed to be a node \textbf{D} here.  I'm expecting a triangle, but get a square.\par \begin{tikzpicture}    \coordinate (A) at (0,0);   \coordinate (B) at (1,0);   \coordinate (C) at (1,1); %  \coordinate (D) at (0,1);    \ifnodedefined{D}     {  \draw (A) foreach \myn in {B,C,D} {  -- (\myn) } --cycle;  }     {  \draw (A) foreach \myn in {B,C}   {  -- (\myn) } --cycle;  }  \end{tikzpicture}  \end{document}   produces: How to remove local (untracked) files from the current Git working tree How do you delete untracked local files from your current working tree? Word style "keep with next" except on last item Riemann and Darboux Integral of a product of two functions Let $f: B(0,1) \rightarrow \mathbb{C}$ be holomorphic and suppose $\exists\ r \in (0,1)$ such that $f$ is injective in $A = \{z \in \mathbb{C} : r &lt; |z| &lt; 1\}$. Prove that $f$ is injective.  I tried using Rouché theorem, or the identity theorem, but I don't know what to do. Any hints? :)