There may be mistakes by grammar since I do not live in English-spoken-world.  I am looking for a book on number theory (in English) . If the book is mainly written about number theory, I do not mind whether one is text or reading.Remark; Reading is book including an anecdote etc.
Books on Number Theory for anyone who loves Mathematics?(Beginner to Advanced &amp; just for someone who has a basic grasp of math)
I have a question about the following text:     Last week Alex Knapp at Forbes published an article criticizing my Nikola Tesla comic. I don't normally respond to these kinds of thing, but since it's' Forbes I figured a proper response was in order.    I would rather say "this kind of things" rather than the version in the text above. Should I mention about my governmental-funded PhD scholarship which I don't want to use How to accomplish SQL Server 2012+2014 high availability Maybe I'm searching for the wrong thing, but I can't see how I can do this.  I have two servers:   Server A (has SQL Server 2012 installed) Server B (has SQL Server 2014 installed)   Server A provides an API via IIS. The code both inserts and gets data from the database depending on the API call.  Server B does exactly the same for its local database.  I would like to have it so that the two databases are consistent copies of each other. I do believe this is what HA accomplishes.   So a load balancer, for example, might direct API calls to A sometimes, and B sometimes, but the data needs to be consistent either way.  I found some documentation on HA for SQL Server 2012, but not on how to do this for a mixed environment of 2012 and 2014.  Any help or pointers to documentation would be great! Thanks. Server login attempts NOT blocked after configuring fail2ban Limit involving the exponential of an expression plus a small-o I'm trying to formalize the following limit:  $$\lim_{x \to \infty} \left[1+\frac{a}{x}+o\left(\frac{1}{x}\right) \right]^x= e^a$$ however I can't see how to rigorously show this identity.  Any suggestions? Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer. Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.   I'm not familiar to factorial and I don't have much idea, can someone show me how to prove this? Thank you. Winter Bash 2019 bugs with the "glasses with a number on top" hat and the "Philanthropist" hat Footnote without a marker What is the relationship between the focal length and field of view for an equal-area ("equisolid") projection fisheye lens?  Alternatively, what is the relationship between the 180-degree image circle size and the focal length for such a lens?  Ultimately I want to find the field of view of a Tokina 10-17 mm fisheye zoom at focal lengths other than 10 mm on APS-C (). Appreciate your wisdom on this,  My understanding is most of the tutorials recommend normalizing / scaling the data prior feeding the tensorflow models. Doesn't normalization require that data conforms to the normal parametric distribution?  What good is a non-linear model if scaling / normalizing is a pre-requisite prior using the non-linear model such as tensorflow?   So back to the question, should I always normalize / scale my data prior feeding my tensorflow models?  thanks Is it possible to install Ubuntu without formatting any partitions? Can I install Ubuntu without formatting any partitions on my hard drive?  I am already running Windows 7 and I want to install Ubuntu as well without formatting any of the partitions I have already created. Apparently this is a  and should hopefully be fixed in an upcoming update.    I have installed SQL Server Management Studio v17.9 on a clean Windows 10 installation.  This associated all .sql files with SSMS.  I want to associate .sql files with a plain text editor (eg: Sublime) but I am unable to change the default application.  I have tried:   Right click .sql file -> Open With -> Sublime + "Always use this program". Settings -> Default Applications by File Type -> Find .sql -> Change to Sublime Right click .sql file -> Properties -> "Change" button -> Sublime. Using ftype via elevated command prompt as seen    In all 3 cases, my selection is not reflected in any way, anywhere.  The icon remains SSMS, and the file opens with SSMS.  Is there some kind of "File Association retention" setting within SSMS I am unaware of?  Edit: I can change the default application for non-SSMS-associated extensions without issue.  Edit: after deleting registry key HKCU\Software\Microsoft\Windows\CurrentVersion\Explorer\FileExts\.sql, .sql files show a VSCode icon:    If I then double-click New Users.sql, it opens with SSMS and a refresh of regedit shows the .sql entry recreated with ssms.exe associated (the icon remains VSCode):    If I then right-click -> open with -> Choose Another App -> Select Sublime and hit "Always use this to open .sql files", it opens with Sublime and a refresh of regedit shows a new "b" entry created for Sublime.  The icon remains VSCode, and double-clicking opens it in SSMS:    If I then delete the a entry for ssms.exe and rename b -> a such that only sublime exists, then double-click the .sql file, it opens with SSMS and generates a new b entry for itself: Windows 8 opens notepad on boot- no startup entry found I just upgraded from windows 7 to windows 8 and everything is working fine except notepad keeps opening on boot with a "access denied" window that comes up as well. I've ran MBAM and removed some junk, I've disabled every "file not found" item in autoruns as well as something that had a text/xml title in it and I've ran CCleaner a few times. Nothing is working, any help is much appreciated! $A \oplus B = A \oplus C$ imply $B = C$? I don't quite yet understand how $\oplus$ (xor) works yet. I know that fundamentally in terms of truth tables it means only 1 value(p or q) can be true, but not both. But when it comes to solving problems with them or proving equalities I have no idea how to use $\oplus$.  For example: I'm trying to do a problem in which I have to prove or disprove with a counterexample whether or not $A \oplus B = A \oplus C$  implies $B = C$ is true.   I know that the venn diagram of $\oplus$ in this case includes the regions of A and B excluding the areas they overlap. And similarly it includes regions of A and C but not the areas they overlap. It would look something like this:    I feel the statement above would be true just by looking at the venn diagram since the area ABC is included in the $\oplus$, but I'm not sure if that's an adequate enough proof.  On the other hand, I could be completely wrong about my reasoning.    Also just for clarity's sake: Would $A\cup B = A \cup C$ and $A \cap B = A \cap C$ be proven in a similar way to show whether or not the conditions imply $B = C$? A counterexample/ proof of this would be appreciated as well. How to measure GPU usage? Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal, but that the set of finite sums of products of elements of I and J is an ideal. This ideal is called the product ideal, and is denoted by IJ.   I want to check if my work on the first part makes any sense. I am not sure if I am picking the right example.  If I let R = Z and I = (2) and J = (3) then I has multiples of 2, and J has multiples of 3  6 will divide the product IJ if we add 2 and 3 though we get 5 in IJ, but I am not sure if 5 Divides IJ. Launch shell scripts from anywhere Is it possible to run my scripts located in ~/scripts from anywhere?  Say i want to run ./scriptname regardless of my current working directory. Why is $ 561 = 3*11*17 $ the smallest Carmichael number? How to implement "select all" check box in HTML? Use second argument for optional first argument if not provided in macro I'm trying to construct a command with one optional and one mandatory argument and I'd like the default if the optional argument is not provided to be #2.   Why does this not work?  (error: Illegal parameter number ...)  \documentclass{article}  \newcommand{\mycommand}[2][#2]{\label{#1}#2} \begin{document} \mycommand{mytext} \end{document}   And what would be a way around it?   EDIT: For clarification of my specific use case: I'm trying to define a command that passes a variable on as an option to an environment along those lines, where myenv can have options like optionone=X or optiontwo=Y so the default for the optional #1 should be optionone=#2 (not literally #2).   \newcommand{\mycommand}[2][optionone=#2]{\begin{myenv}[#1]\input{#2}\end{myenv}}   Maybe there's generally a better approach?   (The environment definition I'm using is from .)