Is the prime factorisation of Carmichael Numbers always Square Free? Is the prime factorisation of carmichael Numbers always square free?  I saw the next theorem in my textbook which would say yes.
Carmichael number square free Show that if $n$ is a , then $n$ is a square-free.  I did this: Let $n= (p^t)(m)$  where $t &gt;1$. Then by modular property,  $$b^p= b \mod n , \,\, b^m= b \mod n$$ Above two equations are also true in$\mod p$, $\mod p^t$. But in$\mod m$, just $b^n=b \mod m$.  And I tried to use CRT But I couldn't.  I think that I've chosen wrong way
Transformer VA Ratings, Power factor, and Pulsed current What exactly goes into a transformer's VA rating? At a fundamental level it seems that there has to be a limit to what the VA rating can represent.  For example if I draw 2 Amps-RMS from the secondary of a 30VA rated transformer at 15 Vrms this makes sense as the maximum Complex Power I can draw. Still, at a power factor of 1 my maximum current in the transformer would be sqrt(2) * 2 Amps.   But what if my power factor is abysmally low (ie in a DC rectifier) due to harmonic distortion and while I still draw 2A-RMS I have brief current spikes of 15 Amps? Surely the transformer's magnetics couldn't handle these spikes as I'd expect the core would saturate.  My question is what is the practical limit for VA ratings of transformers? Would brief current spikes that reduce to only 2A-RMS in this case be fine? Obviously the secondary/primary copper losses play a part in the rating but how do the magnetics factor in?  I ask this because I am designing a simple bench power supply using a 125VA transformer with a 24Vrms secondary and am trying to figure out how much power I can draw before the current spikes into the inductor are too much for the transformer. I also don't want to have to resort to active PFC as I don't want to risk messing up any HVAC PCB design.  Thank you group of units in a topological ring Does "minor revision" mean "accepted with minor revision"? I just received a decision letter from a journal editor (after three rounds of major revision). The letter shows that the reviewers "have asked for some other minor revisions". After getting the minor revision letter, I immediately completed the revision in accordance with the feedback from the reviewers (the suggested changes just involve adding a few sentences) and immediately resubmitted the revision to ScholarOne. A week has passed since I submitted the revision, but the status in ScholarOne remains unchanged. Is this normal? Can I assume that this basically means "acceptance with minor revision"? Thanks for your insight and sharing. What tool can I use to manage the configuration of my Windows Server environments I help manage environments for an application that uses cloud-based Windows server VMs. The application stack consists of Windows Server 2008 and Windows Server 2012, SQL Server 2008, IIS, and SharePoint 2010. I have several environments Dev/Test/Stage/Prod. I am looking for a way to do configuration management of those environments to make sure any environmental changes are applied in a consisent way and there is a way to verify that no changes have been made to one environment that have not been made to other environments.  I have been reading up on Puppet, Chef, etc and I like the idea of doing delcarative configuration management. What is a good method or tool to use to help manage the configuration of these environments. I know a little  about SCCM but it is too expensive for this particular situation although I would still be interested in knowing if it has the capabiltiy to do those things. Indian passport holder. Do I need transit visa in Sydney? For some results returned in Google Search, on the right side it displays the company details, logo, contact numbers, etc...   For example, see the following screenshot:    I'd like to know what contributes to this so that I can try to achieve it for my site too. I’m writing a series of blog posts and I’m finding a little bit of a conundrum. I want the audience that can be manufactured on Medium but I also want the SEO that comes from long form text on my website.  Is there any type of SEO conflict that would arise from putting the exact same posts on both? Can't delete files in trash because they don't exist on OS X 10.6? Something funky happened on one of my external drives and now whenever I plug it in 2 files show up in my Trash.  If I empty the Trash via Finder, nothing happens.  Ditto for the Option+Empty Trash method.  Listing them via Terminal shows them as there  $ sudo ls .Trashes/501 ¶_|íìê&lt;-.b?†            æâù©ìë—‡.*?§   But attempting to rm them or get any information about them shows them as not there  $ sudo ls -F .Trashes/501/ ls: ¶_|íìê&lt;-.b\032†: No such file or directory ls: æâù©ìë—‡.*\026§: No such file or directory  $ sudo rm .Trashes/501/* rm: .Trashes/501/¶_|íìê&lt;-.b\032†: No such file or directory rm: .Trashes/501/æâù©ìë—‡.*\026§: No such file or directory   Any thoughts?  I've never seen anything like this.  Thanks in advance! List AppDomains in Process how to hard-bypass the input of a line driver with a switch? How does Motherboard and CPU affect RAM choice? Proof a $2^n$ by $2^n$ board can be filled using L shaped trominoes and 1 monomino What I am looking for is the equivalent of System.Windows.SystemParameters.WorkArea for the monitor that the window is currently on.  Clarification:  The window in question is WPF, not WinForm. Is adjoint of singular matrix singular? What would be its rank? Let $A$ be a square and singular matrix of order $n$.  Is $\operatorname{adj}(A)$ necessarily singular? What would be the rank of $\operatorname{adj}(A)$? Why this polynomial is irreducible? Let $K=\mathbb{Z}_p(t)$. How to prove $f(x)=x^p-t$ is irreducible in $K[x]$? Defining macros with arguments With newcommand I can define customized command like \ABC. Is there any way to define a command with arguments. For example I want \brat{A}{B} be the same as [\![A,B]\!]. about://(null) popup? I encountered a popup similar to this one this morning while checking the weather report at  in Safari, though I have not been able to reproduce it.  The title is "about://(null)" and the text "Why you no play Candy Crush!!"  The popup occurred twice.  I tapped Cancel both times.  I suspect the source of this is rogue JavaScript in an ad network, judging from the fact that the screenshot below shows it in an ad-supported application, and when I saw it, I was on an ad-supported website.  My phone is not jailbroken.  I'm wondering if anyone is able to identify the source of the popup definitively.  Speculation is running rampant on Apple's support communities and elsewhere, from push notifications (delete Facebook and all your games!) to carrier notifications (which don't work on iPod Touches…), and my gut tells me little of it is helpful.  But I could also be very wrong.  (This is not my screenshot; it comes from .)    UPDATE 1: The Candy Crush people have this to say, but I'm not (yet) convinced there's actually something installed that is to blame:   UPDATE 2: Just reproduced it in the iOS Simulator while clicking around woodtv.com, but I'm not sure how to track it down further from here. How to calculate $$\int_{0}^{\pi/2}{\{\tan(x)\}dx}$$ where $\{x\}$ means the fractional part of $x$. I mentioned the zero points of $\{\tan(x)\}$. $\{\tan(x)\}$ equals to 0 iff $x=\arctan(k)$, $k$ is an integer. I tried to separate it into$$\sum_{k=0}^{\infty}{\int_{\arctan(k)}^{\arctan(k+1)}{(\tan(x)}-k)dx}$$ Then I found it hard to continue. I don't think I am on the right way. Google Drive files opening in new window vs new tab? This might be a duplicate of  but that question is 5 years old and unanswered.  When I'm in drive.google.com and I open a G Suite file (either double-click or select &amp; press enter) in Firefox it opens in a new window whereas in Chrome it opens in a new tab.   Why do they do that? Is this a browser-specific quirk or a Google setting (that I haven't found)? Is there a way to control the behavior? I'd like them both to open in tabs, but presumably the same answer would be relevant in the opposite direction too. How to make \left, \right pairs of delimiter work over multiple lines?