Find the smallest positive integer $n$ such that $\frac n2$ is a perfect square, $\frac n3$ is a perfect cube and $\frac n5$ is a perfect 5th power.
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
How can I vertically align the numerators of two fractions? Determining likely relationship based upon autosomal DNA shared cM How do I remember which units counter which in StarCraft 2? Can't install aircrack-ng Whenever I attempt to install aircrack-ng in terminal I get the following error:  Package aircrack-ng is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source However the following packages replace it:   iw  E: Package 'aircrack-ng' has no installation candidate"   I'm new to Ubuntu and so have no idea what to do. Should my first trip be to the country which issued my Schengen Visa? A common mistake for beginning group theory students is the belief that a quotient of a group $G$ is necessarily isomorphic to a subgroup of $G$.  Is there a characterization of the groups in which this property holds?  If this question is too broad, I might ask if such a characterization exists for $p$-groups.    History: I originally posed the opposite question, regarding groups for which $\exists N\unlhd G\,:\, \not\exists H \unlhd G\, \text{  s.t. } H \cong G/N$, and crossposted this to .  I received an answer there to the (now omitted) peripheral question about probability, which shows that most finite groups probably have this property.  After this, I changed the question to its current state, as this smaller collection of groups is more likely to be characterizable. Do plugin files have to follow a specific convention to be "picked up" by WordPress? Benefits of using backtick (`) in MySQL queries? In MySQL we can create queries with or without the backtick (`) symbol. Example:   SELECT * FROM TEST; SELECT * FROM `TEST`;   Both works fine in mysql-console.  Is there any technical difference between them?  Is there any benefit using (`) over over simple queries? Force applied off center on an object How to make traces on an universal PCB? I hope this question won't be closed as too subjective. I'd like to know best practice - how to make traces on universal PCB's with individual holes without traces (like the following image). My idea is to bend the ends of discrete components and use them to make traces to other components. Is this approach acceptable, or nasty? Although this is called "prototype" PCB, I'd like to use it for my simple final circuits (low frequency, low current applications), because I hope it will save time. Which is the correct gerund clause? 'People's killing animals', or 'People killing animals ... '? How can I remove duplicate rows? Dates and times: "on", "in", "at"? I’m often confused when I speak about times and dates. What is the rule for using on, in, and at in the following sentences?   I will do it ___ Tuesday. We married ___ March. He returned ___ the same day. Every day ___ the same time, I walk the dog. How to escape @ characters in Subversion managed file names? Came across this little practice exercise, and I couldn't properly convince myself of this relation:  Let $X,Y \subset \mathbb{R}^n$ and $g:X\times Y \rightarrow \mathbb{R}$. Show that $$\sup_{y \in Y} \inf_{x \in X}g(x,y) \leq \inf_{x \in X} \sup_{y \in Y} g(x,y).$$  My thinking was starting with $\inf_{x \in X}g(x,\overline{y}) \leq\sup_{y \in Y} g(\overline{x},y)$, but does that even hold for all $\overline{x} \in X$ and $\overline{y} \in Y$? How can I enable shell-escape? I need to enable shell escape for a package that I want to use. What is shell escape exactly, and how do I enable it in my editor or compiling toolchain? Links to answers for different editors/toolchains, in alphabetical order:   AUCTeX (Emacs) ,         Note: this is a FAQ post. Related Meta question: . Please add an answer for your own editor/toolchain if it is missing. Thank you! When adding an answer, please indicate if the setting is permanent or per-document, and/or describe how you can add a button, shortcut, menu item, etc. to make it easy to switch between shell-escape and regular compilation. Gauss law and electric flux Can you please explain me what is electric flux. I know it is $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$, but in many place its given flux means to flow. But how does electric field "flow"? Also if we assume its the electric field lines (can you also specify what exactly are these) are "flowing" how does $\int\mathbf{E}\cdot\mathrm{d}\mathbf{S}$ give the total electric field lines passing through that area? (can you please elaborate when you explain?)  Pls. I know it shouldn't come here but there is no page for electric flux. GNOME has grey bar on top and bottom after upgrade from 17.04 to 17.10, how do I fix it to how it's supposed to look? This is how my desktop looks after the update, the top bar turning grey and the addition of the bottom bar happened after the update.    From my searching of screenshots this does not appear to be how it is supposed to be. Is there any way to fix it? Is there any criterion (theorem or algorithm) to find out a given polynomial $f(x)$ is irreducible over the field $\mathbb{F}_2$? Sci-Fi book female fighter pilot All I remember about the book is that the protagonist was a human female fighter pilot, she has short hair, not sure if it was blond or auburn and she was involved in making peace with the alien race.  The alien race was invading Earth, but because of her they stopped, surrendered and because of her helped Earth improve its technology. I remember that she melded with something and was starting to sort of think like them and lose a bit of her humanity.  It was set in the not too distant future. I believe I read it in the 90s.