Consider the following Diophantine equation: $x^2 + xy + y^2 = n$
The set of integers $n$ expressible as $n=x^2+xy+y^2$
Using "that" and "this" interchangeably I'm trying to create a unit test to test the case for when the timezone changes on a machine because it has been incorrectly set and then corrected.  In the test I need to be able to create DateTime objects in a none local time zone to ensure that people running the test can do so successfully irrespective of where they are located.  From what I can see from the DateTime constructor I can set the TimeZone to be either the local timezone, the UTC timezone or not specified.  How do I create a DateTime with a specific timezone like PST? Getting a credit card exclusively for the sign-up bonus There are quite a few credit cards with exceptional sign-up bonuses (and then fairly average terms). If I signed up for one, fulfilled the spending conditions for the signup bonus, used that bonus, paid off the card and then cancelled it immediately after, would there be a significant impact on my credit history?  I suppose it would divert spending away from my primary credit card (the one I never close), which would reduce slightly the spending history I have on that card. Essentially, the record of my spending on these auxiliary cards would be erased when those cards were canceled. But is there a penalty to my credit score for closing a card beyond the loss of history that was on the closed card? Why do we think of light as a wave? I've read that light travels in a straight line and has a wavelength of 400nm to 700nm. But I don't understand why does it have a wavelength and what creates its wavelength? I agree with the concept of sound which also has wavelength, thus called sound waves which are created by the vibrational movement in air. I'm not aware of calling light a wave. Does the light vibrate too? If so, then how? Is there a video that explains how Stack Overflow works and can be used? Is there a video that explains how Stack Overflow works and can be used? I.e. a short tutorial to get new users started. If there isn't, then the people behind this site or others who know how it works should make one, because it's overwhelmingly different from other sites and thus difficult for beginners. When I search for similar questions that I am going to ask, I usually can't find anything through the search box on Stack Overflow. But when I enter my question on the &quot;Ask Question&quot; page, the questions suggested through the &quot;Questions with similar titles&quot; box are usually relevant. Do you experience the same thing? I haven't had the chance to take any serious low-level programming courses in school. (I know I really should get going on learning the "behind-the-scenes" to be a better programmer.) I appreciate the conveniences of Java, including the ability to stick anything into a System.out.print statement. However, is there any reason why you would want to use System.out.printf instead?   Also, should I avoid print calls like this in "real applications"?  It's probably better to  to print messages to the client's display using some kind of UI function, right? Taylor series expansion for $f(x)=\sqrt{x}$ for $a=1$ How would one format an Excel sheet so numeric fields are set to numeric field types when importing to ArcGIS 10.2? Show finite complement topology is, in fact, a topology Given, $\{x_n\}$ and $\{y_n\}$ are two real valued sequences such that $\lim_{n\to\infty} (x_{n}^{3}-y_{n}^{3})=0 $ Then is it always true that $\lim_{n\to\infty} (x_n-y_n) =0 $ ? I tried by splitting $ (x_{n}^{3}-y_{n}^{3}) $, but that didn't help as $\lim_{n\to \infty} (x_{n}^{2}+x_{n}y_{n}+y_{n}^{2}) $ can be $0$ or non zero or doesn't exist. How does gravity work on Star Wars ships? Inspired by the question , how does gravity work on the Millennium Falcon and other ships its size? The passengers are not strapped in and regularly move around just easily as they would on a planet with Earth's gravity.   The answer for the Death Star refers to gravity often being "coreward" (presumably taking advantage of the natural gravity an object of such substantial mass would have), but that doesn't apply for a small ship. So how is gravity accomplished? I would like to transform 5V 500mA (from USB power) into 12V with a few cheap components.  Is this possible with the help of some generic parts (and not with the help of some expensive transformer, etc.)?  Also, how many milliamps would this provide? What is the width of the standard paragraph indent in LaTeX's article class? If no changes has been made to the settings of indentation of an article class LaTeX document, what is the width of the paragraph indent?  texdoc article in the terminal opens the Standard Document Classes for LaTeX version 2e manual. In section 6.2 Paragraphing I find the following line:  ⟨10pt⟩ \setlength\parindent{15\p@}   The  means 1pt ... so I guess this would mean that the standard indent is 15 pt at a 10 pt text size? Is this correct? Are the review queues planned for the iOS app? How do we know photons have spin 1? Is the Formula Logically Valid? I have a question for my exam and I find it hard to understand.  I have to prove that the following formula is logically valid:    The professor told me to "push" all the symbols inside the brackets, and use the deduction theorem.  But I don't know how to do it, because I can't find the identities to push the "exist" symbol inside the brackets.  Your help is appriciated, thank you.  Alan Does $\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$ occur here? Let $\{a_{mn}\},~m,n \in \Bbb{N}$, be an arbitrary double sequence of real numbers then does the following equality occur always?   $$\sum_{m=1}^{\infty}\sum_{n=1}^{\infty}a_{mn}^3=\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}a_{mn}^3$$   I think there is no reason for the equality of this iterated series in general but I cannot figure out how to construct a counter example. Can anyone please help me how to create a example of $\{a_{mn}\}$ such that the given equality does not hold...!! Random Sample vs. As Large a Sample as Possible? I'm struggling to differentiate scenarios where you would use random sampling vs. getting as large a sample as possible. For instance, one thing I am trying to test is the notion that being in a "home" arena boosts player performance.  I have collected individual football game data for every game over the past 10 years. I have over 34000 observations of players performance during this time span. Would it have been more prudent for me to take a random sample of say, 1000 players over the past 10 years?  I just don't understand why, in the above scenario, I'd take a random sample of 1000 when I can just take all of the players performances from the past 10 years. Order of a group and subsequent subgroups I want to prove that if the order of a group G is greater than 1 and non-prime, then G has a subgroup other than the trivial subgroups {e} and G itself.   I am confused because I am only being able to prove the case for prime order by using Lagrange’s theorem i.e. if I have a group of order p, where p is a prime number, then the order of subgroups must divide p, hence the order can be either 1 or p.   How do I go about proving the case for non prime order let’s say x > 1?