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Refactoring RadioGroup setter code? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$? Is $x^3+y^3+z^3-1$ irreducible over a field $k$ of characteristic $\neq 3$?   If I can show that $y^3+z^3-1$ is irreducible, I believe I can use Eisenstein's criterion. But I don't see how to show even this.  The other approach on my mind is to show that $k[x,y,z]/(x^3+y^3+z^3-1)$ is an integral domain, but this doesn't seem particularly promising either. "One of them was/were you" If I am talking to somebody about a certain group of people in the third person, and then want to refer to the person I am talking with as one of those people, which do I say?     One of them were you      One of them was you. Nielsen & Chuang Exercise 2.2 - “Matrix representations: example” Reproduced from Exercise 2.2 of Nielsen &amp; Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition):     Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$, and $A$ is a linear operator from $V$ to $V$ such that $A|0\rangle = |1\rangle$ and $A|1\rangle = |0\rangle$. Give a matrix representation for $A$, with respect to the input basis $|0\rangle, |1\rangle$, and the output basis $|0\rangle, |1\rangle$. Find input and output bases which give rise to a different matrix representation of $A$.   Note: This question is part of a series attempting to provide worked solutions to the exercises provided in the above book. Sylvester's theorem states that the product of $k$ consecutive integers $&gt;k$ has a prime factor $p&gt;k$. Erdős gave a short proof for it, but I can't find Erdős's proof online. Can anyone give a sketch of the proof? Thanks. I have a Storex eZee Tab 702 tablet. My Google Play Store was working very well until a few weeks ago, when it started saying,     Error while retrieving information from server [DF-DFERH-01]   I tried to clear the cache, clear the data, force stop, and downloading another Google Play Store, but I'm still having the same problem.  How can I fix this issue? Grammar-checking tool for use with LaTeX? I am looking for a grammar-checking tool, i.e., something that checks for mistakes such as "two dog" or "a books".  It has to work on Linux (Ubuntu).  Also, since I use macros to generate some of the prose, it has to somehow work with LaTeX.  I don't think that such checkers are LaTeX-aware, so it has to work with some compilation product of LaTeX: DVI or PDF.    If you suggest a grammar checker that checks plain text, please explain how to you extract the text.  catdvi does a nice job, but it leaves some garbage like page numbers. Prove ${n - 1 \choose k - 1} + {n - 2 \choose k - 1} + {n - 3 \choose k - 1} + \dots + {k - 1 \choose k - 1} = {n \choose k}$ How to pass the values from one activity to previous activity Dividing polynomial $f(x)$ by $x-3$ and $x+6$ leaves respective remainders $7$ and $22$. What's the remainder upon dividing by $(x-3)(x+6)$? Cannot locate Ubuntu Software Center via Firefox to open APT links Most of you if not everybody will agree that the stronger the gravitational pull, the faster an object will fall. For example, on a planet with 50 times the gravity of Earth, any object will hit the ground on that planet much quicker than it would on Earth. So taking all of these into the equation, does it mean that at a blackhole, an object will fall at an infinite speed because of the infinitely strong gravitational pull of the blackhole? Can an LC oscillator be used to generate visible light? The LC oscillator is most commonly used to generate radio waves for practical use and the frequency $\omega$ of the LC oscillator equals that of the electromagnetic wave so produced. So, can they in principle be used to emit visible light?  The frequency of visible light is on the order of a few hundred terahertz, and the frequency of an LC oscillator is   $$\omega = \frac{1}{\sqrt{LC}}$$  I admit, the  product $LC$ does become very small (on the order of $10^{-30}$) when the numbers are plugged in, but making an inductor and a capacitor with small values isn't difficult, is it? Traverse a list in reverse order in Python So I can start from len(collection) and end in collection[0].  I also want to be able to access the loop index. Forcing a SimpleXML Object to a string, regardless of context Why does mathematical convention deal so ineptly with multisets? Why is a ConcurrentModificationException thrown and how to debug it I am using a Collection (a HashMap used indirectly by the JPA, it so happens), but apparently randomly the code throws a ConcurrentModificationException. What is causing it and how do I fix this problem? By using some synchronization, perhaps?  Here is the full stack-trace:  Exception in thread "pool-1-thread-1" java.util.ConcurrentModificationException         at java.util.HashMap$HashIterator.nextEntry(Unknown Source)         at java.util.HashMap$ValueIterator.next(Unknown Source)         at org.hibernate.collection.AbstractPersistentCollection$IteratorProxy.next(AbstractPersistentCollection.java:555)         at org.hibernate.engine.Cascade.cascadeCollectionElements(Cascade.java:296)         at org.hibernate.engine.Cascade.cascadeCollection(Cascade.java:242)         at org.hibernate.engine.Cascade.cascadeAssociation(Cascade.java:219)         at org.hibernate.engine.Cascade.cascadeProperty(Cascade.java:169)         at org.hibernate.engine.Cascade.cascade(Cascade.java:130) Virtual member call in a constructor Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$ I'm working on my Discrete Mathematics homework and they are asking me this:  Prove or show a counterexample for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$  I'm not completely sure how to prove it. I was thinking to find a counterexample like zero but I'm not sure if that it's going to work. Or maybe try to approach it backwards?   I'm a little bit lost Pseudoinverse and norm Suppose the m * n matrix A =$ \begin{bmatrix}     A_1 \\A_2 \end{bmatrix}$ where A1 is a nonsingular square matrix (n*n) and A2 is an arbitrary matrix. Why is $||A^{+}||_2 \leq ||A_1^{-1}||_2$  ?   ($A^{+}$ denotes the psuedoinverse)