Prime numbers of form $a^n-1$.
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
How to change inside background color of UISearchBar component on iOS What term describes a non-offensive substitute for a swear word?   For example, Battlestar Galactica used frack instead of fuck. Another example is the use of snap instead of shit.  I think I may have heard a single-word term used to describe such alternate non-offensive words before, but I don’t know what it is. Titles of articles I'm about to cite contain upper case letters and when using BibTeX it converts them to lower case ones. This happens only in the title and only the first letter conserves its case. For example, when I cite an article about HF, the reader won't know if it is about Hafnium (Hf) or fluorine acid (HF).  I know that I can fix it manually in the .bbl file but I would like to avoid it, or fix it automatically. I have a population of phone calls - 200,000.  There are different reasons for each call, but lets assume the number of reasons is known. i.e. 7 different call reasons: 1) Check on order 2) Cancel order 3) Billing information 4) Account information etc...  My question is, I want to get a statistically significant sample size so the number of calls I listen to in my sample are representative of the distribution of the reasons in the overall population of 200,000 calls.  What should the sample size be? Which methods to use to calculate the sample size? What are post-installation triggers?  These are executed when upgrading software. Proving that a list of perfect square numbers is complete Well, I have a number  $n$ that is given by:  $$n=1+12x^2\left(1+x\right)\tag1$$  I want to find $x\in\mathbb{Z}$ such that $n$ is a perfect square.  I found the following solutions:  $$\left(x,n\right)=\left\{\left(-1,1^2\right),\left(0,1^2\right),\left(1,5^2\right),\left(4,31^2\right),\left(6,55^2\right)\right\}\tag2$$     Is there a way to prove that this a complete set of solutions? So I mean that the solutions given in formula $(2)$ are the only ones?     My work:   We know that: $$ 1 + 12x^2 \left(1+x \right) \ge 0   \space \Longleftrightarrow \space   x \ge -\frac{1+2^{-2/3}+2^{2/3}}{3}   \approx -1.07245 \tag3 $$ So we know that for $x&lt;-1$ there are definitely no solutions. Which is the correct tense to use with 'by'? I gave him the money by 6 PM.   I had given him the money by 6 PM.   I can't spot the difference between them and both seem right, but I was told the first one is wrong. Can anyone say, why?  Here is a another set of sentences with the same issue:     By 5 PM I gave him the book.   By 5 PM I had given him the book.   In both the sentences the book was given before 5 PM and no later than 5 PM. But I can't understand then what the difference between them is.   Is it right to use simple past with 'by' at all? If yes, then why and if not, then why is it incorrect to use simple past with 'by'? Is there a way to log all Microsoft SQL Server queries executed on a certain server, with their respective durations?  I'd like to be able to analyze all queries will a tool like what  does for PostgreSQL. While we're at it: do you know of any such tools? Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule] I am working on a problem I am pretty close to solving but I can't figure out the last part. I used some algebraic manipluation to break the problem down. The problem is:     Show that the following congruence is true      a^b = ((a mod n)^b) (mod n)      for any positive integers a, b, and n.      Hint: Number a can be written as a = q*n + r, where q = floor brackets a/n, and r = a mod n.   My attempt it:     (q*n +r)^b = ((a mod n)^b) * (mod n)      (q*n)^b + (a mod n)^b = ((a mod n) ^b) * (mod n)      (a)^b -(r)^b = ((a mod n) ^b) * (mod n)      (a)^b = modn  ----> divided by ((a mod n)^b)   Am I doing this correctly and if so how can I prove this is true? Is there a trick I am missing? I think that by simplifying it further I would just keep going in a loop.  Thanks! How does the lens diameter influence photo quality? I have tested two different 50mm lenses in my camera. One was a Nikkor 50mm ∅52mm. The other one was a Sigma 50mm ∅72mm. I took some pictures with both lenses using the same setup for aperture and shutter speed, but couldn't notice significant differences in the quality of the pictures.   So, how does the diameter affects the photo quality, if it does? What advantages would the ∅72mm lens have over the ∅52mm one? What's is the origin of Orbital Angular Momentum of electrons in atoms? Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with the probability of finding it being maximum a radial distance $R$ (=Bohr radius) away from the nucleus. This helps explain why the electron does not radiate EM radiation while in the atom.  But, with this understanding, I do not understand the source of the orbital angular momentum. Is it intrinsic like the spin? Obtain screen status using ADB In Unity3D, how do I create an efficient scratch card effect? I want to create a scratch-card-like effect in new Unity UI's new Image tag.  I know it's possible with setPixels, but that's prohibitively expensive on mobile devices.  Something like this:    I'd like the user to be able to drag on any part of the image to "scratch off" the top layer and reveal the content underneath it.  How can I do this? C++11: defining function on std::array How do I unload (reload) a Python module? I have a long-running Python server and would like to be able to upgrade a service without restarting the server. What's the best way do do this?  if foo.py has changed:     unimport foo  &lt;-- How do I do this?     import foo     myfoo = foo.Foo() Migrated questions don't have a user action label in the question list Bash Script if condition is always true I just watched a TV show and the guy says:     I ain't trying to fight with nobody with a baby.   So here, I can't understand the "nobody" since it make no sense to me, but it sounds like anybody, and if it's "I ain't trying to fight with anybody with a baby." that makes sense to me. Wildcard not working in subprocess call using shlex Can we make the "expanded user card" privilege universal? Pursuant to discussion on the , several have asked how far they'll need to search to determine if a user has expressed their preferred pronouns. This requested feature could create an easy solution for that concern.  On sites where I've reached the  privilege level, users can hover over my picture to see a snippet of my profile:    This is where I've included my preferred pronouns, and where I see many others including them as well.  By making this feature universal, users could quickly and easily check for preferred pronouns without needing to navigate to another page.