For $a,b,n,m\in \Bbb N$, if $a$ and $b$ are coprime, than for $m^n=a\cdot b$ $\exists a',b'\in \Bbb N: a=a'^n \land b=b'^n$  I thought it would suffices to show that $m=a'\cdot b'$, but I'm not sure that's why I also thought of : As $a,b$ are coprime than we can write $$\begin{align}a&amp;=p_1^{u_1}\cdots p_i^{u_i}\\b&amp;=q_1^{v_1}\cdots q_j^{v_j}\end{align}$$ where $p_g\neq q_g \forall g$ so$$\quad m^n=a\cdot b=p_1^{u_1}\cdots p_i^{u_i}\cdot q_1^{v_1}\cdots q_j^{v_j}$$ As the $u_i,v_i$ doesn't necessary need to be distinct, we can rewrite to $$m^n=(p_1q_1)^{n_1}\cdots(p_iq_j)^{n_{ij}}$$ we define $m:=\prod p_hq_h$ and $n:=\prod n_{ij}$ Not sure how to continue or either it's correct or not :(
Show that if $n$, $a$, $b$, and $c$ are positive integers with $\gcd(a, b) = 1$ and $ab = c^n$, then there are positive integers $d$, and $e$ such that $a = d^n$ and $b = e^n$.   I know that (by Bezout) $\gcd\left(a,b\right) = 1$ implies $ax + by = 1$ for some integers $x$ and $y$, and also that $\gcd\left(a^n,b^n\right) = 1$, but this does not help me.
Are the leftovers from making stock good for anything? Having made stock and strained it, can the meat and vegetables boiled up in the stock be used for anything, or should they go in the bin? I have read , but it was asked in the context of servers not desktops or notebooks.  If a good amount of RAM is installed on a notebook, say 8 GB, do we still need a swap space? "In" vs. "after" for future talk The class will be over in 10 minutes. The class will be over after 10 minutes.  I know the first is correct but why? Why is there conservation of kinetic energy in elastic collision and not in inelastic collision? gedit "cannot open display" , on remote computer , using ssh - Ubuntu 12.04 Mac Mini (Mid-2011), 16GB SSD, 16GB RAM, El Capitan (v10.11.6)  The Mac ran fine until I upgraded to Sierra. The latest Mac OS conflicted with most of the specialized apps I use every day, So I immediately returned to El Capitan.  Activity monitor shows that two "Installer/Installer.app" items are always running and are they major users of all of my available memory. Consequently, all my others apps become unresponsive.  I run Disk Utility, and the Installer.app show up there as .dmg files; but I cannot erase, delete, or unmount them. None of my 3rd party app can remove the installers.  My Mac Mini, which should be running super-fast (as it used to), now runs dreadfully and disgustingly slow. I a truly upset with Apple for this kind of garbage. To get their help: $$$. Best way to hide a window from the Alt-Tab program switcher? I've been a .NET developer for several years now and this is still one of those things I don't know how to do properly. It's easy to hide a window from the taskbar via a property in both Windows Forms and WPF, but as far as I can tell, this doesn't guarantee (or necessarily even affect) it being hidden from the Alt+↹Tab dialog. I've seen invisible windows show up in Alt+↹Tab, and I'm just wondering what is the best way to guarantee a window will never appear (visible or not) in the Alt+↹Tab dialog.  Update: Please see my posted solution below. I'm not allowed to mark my own answers as the solution, but so far it's the only one that works.  Update 2: There's now a proper solution by Franci Penov that looks pretty good, but haven't tried it out myself. Involves some Win32, but avoids the lame creation of off-screen windows. Proper capitalization of commonly used acronyms and initialisms How to test if my server is vulnerable to the ShellShock bug? How can I ensure my Bash installation is not vulnerable to the  bug anymore after the updates? Variable declaration placement in C Is there a word for someone with the same name? If a person shares my name, in Dutch there is the word &quot;naamgenoot&quot;, meaning roughly 'member of the same name'.  John A: Hi, my name is &quot;John&quot;  John B: O, then we're insert solution word here!  Similarly,  'classmate' is 'klasgenoot' in Dutch 'roommate' is 'kamergenoot' in Dutch  I'm pretty sure I cannot call someone with the same name as mine a 'namemate' :)  Edit Because sceptics appear to be frustrated mightily by an apparent lack of research, there was  in chat, with no satisfactory conclusion. /Merriam Webster namesake appears to be linked to intentional name correspondance (being named after someone). There may be a US/UK English divide there.  &quot;I was named after my grandfather. I am his namesake.&quot; -   Also, the introduction seems to hint at much broader meaning:  &quot;Namesake is a term used to characterize a person, place, thing, quality, action, state, or idea that has the same, or a similar, name to another&quot;   Do you know of a better word/phrase to describe this succinctly? How can I vertically align elements in a div? I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers? &lt;div id=&quot;header&quot;&gt;   &lt;img src=&quot;..&quot; &gt;&lt;/img&gt;   &lt;h1&gt;testing...&lt;/h1&gt;   &lt;img src=&quot;...&quot;&gt;&lt;/img&gt; &lt;/div&gt; Indentation of continued lines in algorithmicx Trying to get the indentation right within the algorithmic environment I run into trouble, and all the solutions posted so far have not been able to solve my problem as I'd like to see it solved.  I want continued lines to have an indentation w.r.t the initial line (new to this forum and yet unable to post images).  However, the best I get with what I've found on this forum is either a fixed indentation for all continued lines (i.e., no difference if the initial line was indented or not), or the same indentation as the initial line (see MWE below).  Anybody has an answer to this?  \documentclass[10pt, A4]{report} \usepackage{algorithm} \usepackage{algpseudocode}  \begin{document}  \begin{algorithmic}\raggedright  \State Define N\_crf as the number of points on the circumference of the hyperstreamline, which will define its cross-sectional area at each r  \For {n = 1 : number of tracts}  \State \parbox[t]{\dimexpr\linewidth-\algorithmicindent\relax}{define N\_crf points creating a unit circle around r(n,i), in the plane perpendicular to t(n,i).}\strut  \EndFor  \end{algorithmic}  \end{document} What does % do to strings in Python? Whether and how to thank a girlfriend or boyfriend in the acknowledgements of thesis? Tell rate-limited users how long they have to wait before asking a new question New users are limited to one question per an hour, but once they'll hit this limit, all they see is You can only post once every 60 minutes. I think it would be very appreciate to change / extend this message, adding You need to wait next xx minutes. I saw similar solutions on many forums.  Would it be hard to implement something like that?  EDIT: It could be either added as extension to above mentioned warning message or as red-colored reminder above Title field. Or even as an explanation message, preventing user from clicking on a Ask Question button? Anything would be good, to not let user write the question (can be time consuming) only to hit the wall of limit. This can be a little bit annoying or frustrating, don't you think? What is the Python equivalent of Perl's chomp function, which removes the last character of a string if it is a newline? I have a vocabulary like this:   Parent 1  Child 1 Child 2 Child 3   Parent 2  Child 1 Child 2    Now I would like to use a view to create a list of a Parent term with its Child terms. I try to do this with Views UI, but only show the term parent... No the child term's. It is very confusing for me.  Can anyone help with this case? Thanks :D How can I tell what RAM will fit my computer? If I want to add more RAM to my computer, how can I buy something compatible? What kinds are there? How do I determine which kind my computer will accept and how much I can add? I'm running macOS 10.15 Catalina Beta.  When I try to install Spotify I see the following error:    Is this a Spotify issue or a Catalina issue?  Thanks.