Multivariate Polynomial Division Question
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
I'm here with weird stuff again.  How can i continue numbering while changing numbering style to Arabic from Roman? For example let's assume I have total of 7 pages and I want to number the first 3 of them as : i,ii,iii; then I change back to Arabic again and continue counting as 4,5,6,7. Can markdown icons be available on the iPad? As you can see by the screenshot below, neither buttons nor even the live-preview is available on the iPad.    StackExchange is great on mobile devices, maybe it can be full available in mobile safari as well.  The same thing happens with the tags autocomplete, there is no options for it! we need to check previous questions to know what tags are available to use. Why do I get "Exception; must be caught or declared to be thrown" when I try to compile my Java code? Can US citizens go to Cuba freely and vice versa after the recent diplomatic relation restoration? A recent full diplomatic relation restoration between the US and Cuba took place, does that mean that US citizens can go to Cuba freely and vice versa? I'm trying Google's PageSpeed online service  Ironically, it's primarily highlighting Google's own services as something that needs improvement on my site  1) jQuery from Google: blocking. So I moved all javascript from &lt;head&gt; to the end of the document before &lt;/body&gt;. That helped  2) Linking to external Google Font CSS (in &lt;head&gt;): blocking. But the font is critical to the design of the page and should load before much else  3) Google Analytics: Caching is not good. (Google has set it internally to 2 hours expiration). Don't know how to change this (this is also placed at the bottom of page)  The Google Font is highlighted as a big priority to change.  How can I fix this? Where/how should I call the the font? Determiners: anyone versus someone Using a new document class/template with LyX? I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next? Is there an easy way to add a hole into an object? If I wanted to add a hole into an object e.g. Create a tube  Is there an easy way to do that?  I haven't seen anything regarding negative space so far in Blender, and it would be really helpful for my project  Thanks in advance! "To do this" or "For doing this" to start explaining something? Many questions have been asked and answered about "to + bare infinitive" vs "for + gerund" in the middle of a sentence.  However, when one wants to start explaining something, what is better? For instance:  "Now, let us focus on baking the bread.   To do this, start by turning the oven on.", or For doing this, start by turning the oven on."?   Are there even better expressions? I have not found anything concerning this situation, and I feel that the answers about the same problem but in the middle of a sentence do not apply here. Why is $ 561 = 3*11*17 $ the smallest Carmichael number? Is there an GUI Designer for python? Is there a GUI IDE for programming python just like java has netbeans?  I wanted one where we could drag &amp; drop test boxes &amp; labels just as we do in swing components using netbeans or eclipse.  Or is there an add-on present in either netbeans or eclipse itself? How can I convert byte size into a human-readable format in Java? Anomalous community user activity On the meta home page I noticed the  is listed as doing something, but cannot figure out what it is.  There is nothing on the  or its , but the recent activity is listed with the same timestamp. I am following Carroll's GR book. He explain that it is convention to parameterize geodesics of photons by a parameter $\lambda$ such that  $$p^\mu ~=~ \frac{d x^{\mu}}{d \lambda}.\tag{3.62}$$  But this is the definition of 4-velocity for a massive particle in the case of $\lambda=\tau$ equal to proper time. My question then, is $$u^\mu = p^\mu$$ for all massless particles? I ask because it's well-known that proper time $\tau$ freezes for massless particles. A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian? Let $(G,.)$ be a group and $m,n \in\mathbb Z$ such that $\gcd(m,n)=1$. Assume that $$ \forall a,b \in G, \,a^mb^m=b^ma^m,$$ $$\forall a,b \in G, \, a^nb^n=b^na^n.$$  Then how prove $G$ is an abelian group?  Some context: Some of these commutation relations often imply that $G$ is abelian, for example , or . This looks like another example of this phenomenon, but the same techniques do not apply. I'm trying to get a Schengen Visa from my first port of entry, France. I am trying to book an appointment with the French Consulate in SF, and the URL I am using is the following:   I've been checking this page periodically for the past few weeks, and I always see a dialog that that says "We are currently at full capacity. Please try again later." Their calendar provides no direct option for going to the next month. (Using the in-browser developer tools, I noticed that the button for next month is hidden. Un-hiding it and clicking on the Next Month button displays no available appointments either. I checked all the way until September 2016).  My guess is that there are absolutely no appointments for the next 6 months. Or, more likely, their page isn't functioning properly. I'll be traveling in July. Does anybody have any alternate suggestions to book an appointment? Proving by induction that $\sum\limits_{k=2}^n \frac1{k^2}\le 1$ Keep processes running after SSH session disconnects Removing clock from the lock-screen I'm using Ubuntu 18.04.  I want to remove the digital clock from the lock screen because I just want to see a good wallpaper there, unobstructed.   How do I go about this? Gedit has a transparent background since upgrade to 16.10 Since I upgraded to from 16.04 to 16.10, gedit has strange new "feature": its background is totally transparent.    Where can this come from ?  Notice I'm using Unity and don't have any specific gnome package installed besides what comes by default. Notice also that in 16.04 I used the Vivacious theme from ravefinity PPA, but I had to go back to Ambiance as Vivacious was broken in 16.10. Maybe it's related.  [EDIT] changing the 'Fonts and Colors' in gedit to any theme other than default (Kate, Solarized, Oblivion, etc..) solves the issue. So there must be a faulty gtksourview file in my home somewhare, but I can't find it...