Prime ideals of the ring of integers lying over $p\mathbb{Z}$
Can infinitely many primes lie over a prime?
How can mixed content compromise an entire HTTPS session? Where can I ask about Software Licenses/Licensing? cant install or remove anything on 18.04 cause of DPKG error Sometimes it is convenient to refer to a group of equations by a letter and a number.  For example:   2+1   (A1) 2+4   (A2) x^4   (B3) x^e   (B4)   Placing  \tag{A\theequation}\label{eqn:thisone}\stepcounter{equation}} instead of just \label{eqn:thisone} works, but seems hacky (especially manually stepping the counter).   Is there a better way? Using thematic layer for segmentation in eCognition? I have a thematic layer, i want to perform segmentation and classification only within the thematic layer,not in a whole image. how can i do it? I tried to segment the image after viewing the thematic layer in view setting and the thematic layer usage was enabled, but it was segmenting the whole image. I'm programming a presentation in LaTeX using the beamer class.  However, it defaults to 4:3 aspect ratio slides, while everything I use is 16:9. Is there an easy way to change this using a command or two? Values of the limit $\lim\limits_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$ Hi I have a question regarding finding the values of limit for the following question.  Let $a, b \in \mathbb R$. Find the limit $$\lim_{x\to+\infty}\left(\sqrt{(x+a)(x+b)}-x\right)$$ I've deleted a system file from my Mac and need to get it back.  System files can include:   hidden files in the root of / - especially unix files in /private  /System files /Library files /Applications files that ship with the core OS   System files are not any app, user files or files that can be regenerated by a known sequence such as cache files, Spotlight index files, etc…    Canonical question and answer for . Is the sum and difference of two irrationals always irrational? If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational? If that's not possible, then a way to trigger the Dock on the screen with mouse without moving my cursor to the bottom of the screen is also an acceptable solution (I know that the launchpad appears on the screen with Dock)  Also i did see the  about this. What's the simplest way to wrap extruded text around a cylinder? What's the simplest way to wrap extruded text around a cylinder that has a specific radius (for example, the label on a can of baked beans)?  I've tried using the Simple Deform modifier, but that (a) doesn't allow you to choose a radius and (b) requires the text to be converted to a curve.  I'm trying to model a cylinder with radius of 30, which has a line of embossed text that runs around the curved side, facing outward.  Thanks! What species of insect is this? I saw this insect near a beach in Corsica France: is uniform convergent sequence leads to bounded function? Suppose there is there is uniform convergent sequence $(f_n)$ on the set $A$, and each $f_n$ is bounded on $A$, i.e., there exist $M_n&gt;0$ such that $|f_n(x)|\le M_n$ for all $x\in A$ Is it true that there exist a function $f$ that is bounded on set A? Can I prove it this way:  Since $f_n \to f$ uniformly on A, $\exists n \ge N$ such that $$|f_N(x) - f(x)| \le 1$$ and $$|f_n(x)-f_N(x)| \le 1$$  Therefore, $|f(x)| \le |f_N(x)|+1 \le M_N + 1$ and $|f_n(x)| \le |f_N(x)| + 1 \le M_N + 1$, $x \in A , n \ge N$  Let $M = \max\{M_1, M_2,\dots,M_N\} + 1$ : $|f_n(x)| \le M$, $\forall x\in A$  Therefore, $f$ is a bounded function on A. Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$ I know how to prove the fact that $ p$ | ${ p \choose k } $ (when writing it as a fraction, $p$ cannot be divided by any of the $1\times2\times...\times k$ or $1\times2\times...\times(p-k)$ because $p$ is prime).  When I try to apply the same rationale for $ p$ | ${ p^n \choose k } $ I get stumped because $p^n$ is in fact divisible by one of the $k! = 1\times2\times...\times k$, where $0 &lt; k &lt; p^n$.  If we take the example of $2^3$ and $k = 7$, we can easily see that $k! = 1 \times 2 \times ... \times 6 \times 7$, and $2$ clearly divides $2^3$.  How else can I approach this? For instance if me and my friend had a Pidgeot and we powered them all the way up. Could mine end up with like 525 and his at like 500? My Developer Account cannot be activated because I used a relative's credit card Suppose $\sum a_n$ converges absolutely and $\sum b_n$ converges. Give an example where the Cauchy product does not converge absolutely. Problem:  Suppose $\sum_{n=0}^{\infty} a_n$ converges absolutely and $\sum_{n=0}^{\infty} b_n$ converges. Give an example where the Cauchy product, defined as $\sum_{n=0}^{\infty} c_n$ where $c_n=\sum_{k=0}^{n} a_k b_{n-k}$, does not converge absolutely.  Question:  I have been scratching my head over this for a while. What would an example be? Unable to modify files/folders in NTFS partition Einstein-Hilbert action as an effective field theory I have read the following statement:      "The Einstein-Hilbert action can be seen as an effective field theory: setting $g_{\mu\nu}= \eta_{\mu\nu}+h_{\mu\nu}$, one gets a free Lagrangian for the field $h_{\mu\nu}$ plus interactions."   Now, how is it possible to define all the interaction terms?  EDIT: I ask apologize if my statement was appeared unclear: I have created a  which is more precise; please don't continue to consider seriously this one. I ran into an interesting behavior recently.  It seems that if I override .equals() to take a parameter other than Object, it doesn't get called.  Can anyone explain to me why this is happening?  It seems to violate my understanding of polymorphism in OOP, but maybe I'm missing something.  Here's much simpler code that shows what I'm seeing:  public class MyClass {   private int x;   public MyClass(int n) { x = n; }   public boolean equals(Object o) { return false; }   public boolean equals(MyClass mc) { return x == mc.x; }   public static void main(String[] args) {     List&lt;MyClass&gt; list = new ArrayList&lt;MyClass&gt;();     list.add(new MyClass(3));     System.out.println("Contains 3? " + list.contains(new MyClass(3)));   } }   When this is run, it prints "Contains 3? false".  It looks like the equals(Object) function is called, even though there is another that would work.  By contrast, if I write equals like this the code works as expected:  public boolean equals(Object o) {   if(!(o instanceof MyClass))     return false;   MyClass mc = (MyClass)o;   return x == mc.x; }   Why isn't it figuring out which version of the function to call based on the type of the parameter?