gcd between powers of two co-prime numbers
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
Assign points within 150 meter buffer of each other the same unique identifier? I have a bunch of points on a QGIS map. Each point is a unique sampling event. However, some of these points have been sampled multiple times but there is no common identifier in the attribute data to determine this. The only way we can see this is by looking at the map and seeing points very close to each other.   I am wondering if anyone has a method to assign points within a 150 meters of each other a common identifier? How do I specify unique constraint for multiple columns in MySQL? Should I use a comma in this sentence? I am trying to teach myself punctuation rules. I have this sentence:     The Disney version generally considered both racist and sexist portrayed the female characters in stereotypical roles and presented ethnically diverse characters with stereotypical features.   I think the sentence needs a comma after sexist and before portrayed. I also think it needs a comma after roles because of what I have identified as a coordinating conjunction. I.e.:     The Disney version generally considered both racist and sexist, portrayed the female characters in stereotypical roles, and presented ethnically diverse characters with stereotypical features.   Did I punctuate the sentence correctly? Is this a coordinating conjunction? Where does TREE(n) sit on the Fast Growing Hierarchy? I currently only have remote access to this CentOS box, I need to move /var form the primary RAID to a new set of disks that was installed with more space, My current thoughts on how to accomplish this is to temporarily mount the new RAID to /tmp/var. rsync everything from /var to /temp/var then modify the fstab to point /var at the new disks.  Here is my question. how do I delete the existing /var on the primary disks once I have the new disks mounted to that location (assuming this is even possible remotely)? How can I get my usual interface when opening projects created by other people? I've bougth cup models from internet.   In the ZIP I get the blend file and pressing F12 I can render the project (Do you call it project?)  But I don't see anymore the "Layout" tab, that is what I use the most.   Why and how can I go back to my usual interface?    Like in the Opening Layout:    UPDATE 1  I could open the file with the default layout, however I'm not seeing the objects in there:    UPDATE 2  How to open Collection 1? It's grayed out. How do I change which mirror I get updates and software from? Relativity and Galaxy Rotation Speed When is it appropriate to use the original pronunciation of a foreign word versus the English pronunciation? When reading to an audience, or speaking in conversation, when is it appropriate to use the original pronunciation of a foreign word versus the English pronunciation (assuming you know the appropriate pronunciation for it)? Is it considered rude, or condescending? Or is it considered a mark of being knowledgeable?  One of the things to consider are place names. When referring to Paris, France, should it be pronounced with the silent 'S' as the French would say it, or with the 'S'? Should Hiroshima be pronounced as a Japanese speaker would pronounce it slightly more emphasis on RO, rather than the SHI? Should Mount Pinatubo be pronounced as a Filipino speaker would pronounce it with shorter stronger vowels, or the longer vowels? (e.g. Pi as is 'pick' rather than 'pea'.) Should Wichita be pronounces as the original "shi" rather than the modern "chi"?  Pronounce pesos or sombrero as a Spanish speaker 'eh' or the English 'ay'?  (I can't think of other common words right now that aren't words taken from other languages like hurricane, boondocks, tornado, etc. which I think have (correctly) changed to English pronunciations.) What word means what many people think 'ironic' means? 'Ironic' is often used to mean an unusual coincidence rather than its true meaning which is closer to sarcastic. That being said, is there a word that would be a good replacement for what many people seem to think it means? How do I make ditto marks? In France, students are taught not to repeat the same text twice when there is little difference between a line and the one below. It's a quick way to take notes.  I reproduced this effect by tinkering:    The code is as follows:  \documentclass[aspectratio=1610]{beamer}  \usepackage[T1]{fontenc} \usepackage[french]{babel}  \usepackage{amsmath, amsfonts, amssymb} \usefonttheme[onlymath]{serif}  \begin{document} \begin{frame} Lorsque le \og \textit{carreau carré} \fg{}   mesure: \begin{itemize} \item $\rm 1\,cm$ de côté, l'unité d'aire est appelée le \og \textrm{centimètre carré} \fg{} et est noté $\rm cm^2$; \item $\rm 1\,dm$ \hspace{1mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}''\hspace{8mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{décimètre carré} \fg{} \hspace{2mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1.5mm} $\rm dm^2$; \item $\rm 1\,m$ \hspace{3mm}'' \hspace{3mm}'' \hspace{8mm}'' \hspace{8mm}'' \hspace{5mm}'' \hspace{7mm}'' \hspace{5.5mm}''\hspace{1mm} \og \textrm{mètre carré} \fg{}  \hspace{9mm}'' \hspace{2mm}'' \hspace{4mm}'' \hspace{1mm} $\rm m^2$; \item etc. \end{itemize} \end{frame} \end{document}   How can I get the same effect more simply than by tinkering like I just did? What is the term for replacing a name or brand with a funny pejorative / sardonicism? What is the term for when one replaces a well-known name [(Proper) noun, company, brand, etc.] with one that tries to be funny yet pejoratively descriptive, different but similar enough that one's audience can likely understand the replacement?  For example: Whole Foods ===> Whole Paycheck; Comcast ==> Scumcast; Starbucks ==> Charbucks; Kinko's == Stinko's; eBay ==> Evil Bay  I tend to use sobriquet don't believe this explicitly implies funny as well as insulting. Moniker again is close but not specific to the above description.  There is a similar question which proposes tortonym and malapropsim, but it does not seem to settle the argument definitively:   Another answer here proposes dysphemism, but to me it isn't a full fit:  because it doesn't cover the humor aspect. Add a linebreak in an HTML text area How can i add a line break to the text area in a html page? i use VB.net for server side coding. Let $x$ and $y$ be positive integers such that $xy \mid  x^2+y^2+1$. Show that $$ \frac{x^2+y^2+1}{xy}= 3 \;.$$ I have been solving this for a week and I do not know how to prove the statement. I saw this in a book and I am greatly challenged. Can anyone give me a hint on how to attack the problem? thanks I'm new to QGIS and have no programming skills.  Is there an easy/uncomplicated way to create multiple buffers around a line feature? Can $\frac{\sqrt{3}}{\sin20^{\circ}}-\frac{1}{\cos20^{\circ}}$ have two values? When going to any page of  with a new reputation gain, the achievements dropdown keeps showing a new badge green highlight:    And then trying to dismiss the notification by clicking on it gets rid of the green badge notification, but the +5 remains even after I've clicked away from the dropdown. Is changing your passport a good strategy for removing a negative immigration history in Schengen? When certain nationalities of people want to travel in the Schengen zone, they are required to apply for a Schengen visa. This is a straight-forward process for most, but when an applicant has had problems with removals or refusals they may be reluctant to apply because they want to avoid the complexities of serial visa refusals. This reluctance may lead some into wondering how their history can be expunged, and this line of thought inevitably leads to the idea of getting their passport replaced with a new one.  This sounds like a great formula for people who have had prior refusals or removals.  In essence they can become 'reincarnated' as a first-time traveller and hence avoid the unpleasantness of revealing their prior interactions with the Schengen authorities.  The relevant parts of the application form are shown here...    Nothing asks about a prior removal or refusal, and the applicant is left with simple denials for 3 questions in order to present themselves as a first-time traveller.  Assuming the person is happy to set aside the moral issues associated with denying their history, are there any holes to this strategy?  This question is scoped to Schengen visa applications so that it will not be unmanageably broad, but answers from other regimes (particularly the affluent Commonwealth and the USA) are acceptable as long as the main points are relatively consistent with Schengen. I noticed that I have three warnings when I submitted my Sitemap. They all say this:      When we tested a sample of URLs from your Sitemap, we found that some   URLs redirect to other locations. We recommend that your Sitemap   contain URLs that point to the final destination (the redirect target)   instead of redirecting to another URL.   I'd like to try and resolve this issues but I'm not sure what to do.  Sitemap url for reference: How to Evaluate $\int e^{2x}\sin(3x)\ dx$? Integration by parts - unless I'm not thinking straight - doesn't seem to help here.. If I pick either of the functions $e^{2x}$ or $\sin(3x)$ to be $u$ or $dv$, they don't change to anything easier... $e^{2x}$ stays in the form $e^x$ and $\sin(3x)$ flip-flops between $\sin(3x)$ and $\cos(3x)$, neglecting the constant that gets introduced.  So how can I approach solving this? $u$-substitution doesn't seem to be something I can use either.