Story about a Kid tagged for lobotomy who hacks the system to become a city executive
Identify this novel: youngsters psychologically tested for abilities/profession, hero wants to author the tests, society uses moving walkways
How to setup a restricted SFTP server on Ubuntu? I would like to know how to set up root, sudo, sftp-only user accounts which won't be required public key authentication at log in. I would also like to know how to set up sftp-only users' home directories where they can't access upper level other directories. What is the radius of convergence of $\sum z^{n!}$? How to find the radius of convergence of $\sum z^{n!}$?   I'm used to applying the ratio test to power series of the form $\sum a_{n}z^{n}$, but for a different power of $z$, I am a bit stumped. What about $\sum z^{2n+a}$ for another example? Where $a\in \mathbb{R}$. So from what I remember it was on cable TV. The main hero was a TV actor zapped to a alien planet. It had a evil overlord with a virgin priestesses. She wants to get laid but he refuses because the next priestesses is only three. Regardless it's a parody things include a man who was maimed by the evil overlord wants revenge the hero eventually screws the virgin priestesses it cuts to scenes of a train going into a tunnel and a volcano erupting. When is it appropriate to use a hyphen? Comparison of backup tools In Group theory proofs what is meant by "well defined" What is exactly meant or required for a mapping to be well defined. I was reading the first Homomorphism theorem () and the first thing the proof does is define a map and find it if its well defined.  Intuitively it makes sense, but what are the requirements for a map to be well defined? For example in the link given, I understand they show one-one relationship as being well defined and later on they again prove its injective.   What have I understood wrongly?  Soham Difference between systemctl and service commands systemd gives us the systemctl commands suite which is mostly used to enable services to start at boot time. We can also start, stop, reload, restart and check status of services with the help of systemctl.  We can do, for example, sudo systemctl enable service_name, and service_name will automatically start at boot time. We can also disable services not to start at boot time.  Is the only difference between the service and systemctl commands that systemctl can be used to enable the start of services at run time? Can we use systemctl on any service? What other significant differences are there? What does the term "BODMAS" mean? What is BODMAS and why is it useful in programming? My Sophix tablet was working without the SD card, but now the camera will not work. I get the following error message:     Insert a SD card before using. Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$ I don't think I fully understand.  Let's say there is a root $x_0 \in K=\mathbb{F}_p(t)$, where $p$ is a prime number.  Then $x_0 = \frac{P(t)}{Q(t)}$ for some polynomials $P,Q \in \mathbb{F}_p[t]$. We can assume $\gcd(P,Q)=1$  and $x_0^p-t= \frac{(P(t))^p}{(Q(t))^p}-t= \frac{P(t)^p-tQ(t)^p}{Q(t)^p} =0$, so coefficients of $P(t)^p, tQ(t)^p$ must be identical, which contradicts $\gcd(P,Q)=1$,   hence such $x_0$ does not exist and the polynomial has no root in $K$.   am I about right?    anyway, I would appreciate an explanation about $\mathbb{F}_p(t)$, what is $t$? what is the meaning of a variable which does not belong to any specific "world"? I cannot use $t$ as if it was a member of $\mathbb{F}_p$ and hence cannot assume $t^{p-1} = 1 \pmod p$... I have an older Nvidia video card and my PC crashes when installing the driver for the video card in Ubuntu 16.04. When I get to the login screen but no further: after entering my password, the system went into a loop and returned always back to the login screen [with funny stripes present].   How do I fix this problem? This is the proof from the book:     Theorem. There are infinitely many primes of the form $4n+3$.    Lemma. If $a$ and $b$ are integers, both of the form $4n + 1$, then the product $ab$ is also in this form.  Proof of Theorem: Let assume that there are only a finite number of primes of the form $4n + 3$, say  $$p_0, p_1, p_2, \ldots, p_r.$$ Let $$Q = 4p_1p_2p_3\cdots p_r + 3.$$ Then there is at least one prime in the factorization of $Q$ of the form $4n + 3$. Otherwise, all of these primes would be of the form $4n + 1$, and by the Lemma above, this would imply that $Q$ would also be of this form, which is a contradiction. However, none of the prime $p_0, p_1,\ldots, p_n$ divides $Q$. The prime $3$ does not divide $Q$, for if $3|Q$  then $$3|(Q-3) = 4p_1p_2p_3\cdots p_r,$$ which is a contradiction. Likewise, none of the primes $p_j$ can divides $Q$, because $p_j | Q$ implies $p_j | ( Q - 4p_1p_2\cdots p_r ) = 3$, which is absurd. Hence, there are infinitely many primes of the form $4n +3$.   END  From "however, none of the prime ...." to the end, I totally lost!    My questions:   Is the author assuming $Q$ is prime or is not? Why none of the primes $p_0, p_1,\ldots, p_r$ divide $Q$? Based on what argument?     Can anyone share me a better proof?     Thanks. How to recover a dropped stash in Git? I frequently use git stash and git stash pop to save and restore changes in my working tree. Yesterday I had some changes in my working tree that I had stashed and popped, and then I made more changes to my working tree. I'd like to go back and review yesterday's stashed changes, but git stash pop appears to remove all references to the associated commit.  I know that if I use git stash then .git/refs/stash contains the reference of the commit used to create the stash. And .git/logs/refs/stash contains the whole stash. But those references are gone after git stash pop. I know that the commit is still in my repository somewhere, but I don't know what it was.  Is there an easy way to recover yesterday's stash commit reference?  Note that this isn't critical for me today because I have daily backups and can go back to yesterday's working tree to get my changes. I'm asking because there must be an easier way! Keep values selected after form submission Restarting with new account on iOS/GameCenter How was Loki not crushed by Mjolnir? Claim: If $(x_\alpha)_{\alpha\in A}$ is a collection of real numbers $x_\alpha\in [0,\infty]$ such that $\sum_{\alpha\in A}x_\alpha&lt;\infty$, then $x_\alpha=0$ for all but at most countably many $\alpha\in A$ ($A$ need not be countable).  Proof: Let $\sum_{\alpha\in A}x_\alpha=M&lt;\infty$. Consider $S_n=\{\alpha\in A \mid x_\alpha&gt;1/n\}$.  Then $M\geq\sum_{\alpha\in S_n}x_\alpha&gt;\sum_{\alpha\in S_n}1/n=\frac{N}{n}$, where $N\in\mathbb{N}\cup\{\infty\}$ is the number of elements in $S_n$.  Thus $S_n$ has at most $Mn$ elements.   Hence $\{\alpha\in A \mid x_\alpha&gt;0\}=\bigcup_{n\in\mathbb{N}}S_n$ is countable as the countable union of finite sets. $\square$  First, is my proof correct? Second, are there more concise/elegant proofs? Does $\sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}}$ converge? Does the following series converge or diverge? $$ \sum\limits_{n=1}^\infty\frac{1}{\sqrt{n}+\sqrt{n+1}} $$ The methods I have at my disposal are geometric and harmonic series, comparison test, limit comparison test, and the ratio test. I gave my friend  as a brainteaser; while her attempted solution didn't work, it raised an interesting question.  I flip a fair coin repeatedly and record the results.  I stop as soon as the number of heads is equal to twice the number of tails (for example, I will stop after seeing HHT or THTHHH or TTTHHHHHH).  What's the probability that I never stop?  I've tried to just compute the answer directly, but the terms got ugly pretty quickly.  I'm hoping for a hint towards a slick solution, but I will keep trying to brute force an answer in the meantime. What is Kirito's relationship with the girls of SAO?