Suppose that $a, m$ and $n$ are positive integers such that $(m, n)=1$. If $m\mid a$ and $n\mid a$, then $mn\mid a$.
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
Trying to understand what happens with a brokerage firm's customers when it goes bankrupt (case of study: Lehman Brothers) I'm trying to understand how secure it is to own mutual funds/ETFs, not in terms of market volatility etc., but in terms of judicial security (i.e. what happens to your holdings if the firm goes bankrupt). To understand it, I have read this article about the bankruptcy of Lehman Brothers:  Note: From now on, I'm always referring to investors who own funds/ETFs managed by Lehman Brothers, not by investors who invested in Lehman Brothers or subprime mortgages (e.g. S&amp;P 500 ETF investors). From the above article, what I have understood is that the funds/ETFs managed by Lehman Bros. were shifted to other brokerage firms to be managed by them. Is this what actually happened? Still, what happens with the investors if, hypothetically, no brokerage firm in the world wants to manage these financial products? Can awakened mind be used with suggestion? Can the warlock class feature "awakened mind" be used in conjunction with the suggestion spell, allowing the warlock to make the suggestion telepathically?  Awakened Mind, Player's Handbook p. 110:     You can telepathically speak to any creature you can see within 30 feet of you. You don't need to share a language with the creature for it to understand your telepathic utterances.   Suggestion, Player's Handbook p. 279:     You suggest a course of activity (limited to a sentence or two) and magically influence a creature you can see within range that can hear and understand you.   If it works with suggestion, would it also work with mass suggestion?  To be clear, I am not asking about the verbal component of the spell, only the method the caster "suggests a course of activity". When testing the difference between 2 proportions why do we use a z-test rather than a t-test?    Further, is there a simple way to conduct an omnibus test for significant differences between more than 2 proportions (in the form of percentages). Is there an equivalent to a one-way ANOVA for this?  I imagine that you could use logistic regression (assuming you have the original data for the proportions in the form of 0s and 1s) Are there other options? Defining my own None-like Python constant Another layman blackhole question, pulling one end of a string out from behind the event horizon No long explanation is needed,  What would happen if I were to allow one end of a rope to fall past the event horizon of a black hole while I held the other end?  Would I be able to pull it out? Would the rope feel extremely (infinitely?) heavy? I'm trying to give the best experience to users of a very huge system (like a CRM). It has a lot of forms and much of these have a lot of fields. My doubt is about if I should use a single column form (which raises too much vertical scrolling), or a two columns form (which needs less vertical scrolling and uses more horizontal white space) and a last one with four columns (which has few scrolling and uses almost whole white space to try to keep most of the fields above the fold).  It's important to say that our clients hate scrolling, and they always ask why we don't use the horizontal white space when we present a one column form).  So I'm little bit confused about it, because a lot of UX studies and good practices recommend to do not use/avoid multicolumn forms but the clients most of times ask multi column forms.  Our clients are very used to desktop programs and not everybody is very familiar with web based systems.  Below follows some possibilities I would like to share to illustrate an example of a complex form in the system with the three possibilities I mentioned:    In the example above I'm using the one column form (most recommended in UX studies), but with a very long vertical scroll.    In the second example I tried to reduce vertical space by using two columns.    This is the client's favorite one, 4 columns using white space and trying to keep everything above the fold.   The lengths of fields are based on the average of characters amount for each field.   I would like to know your opinion about the best approach to this case. Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$ $$GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$$  This is trivial to prove with the first isomorphism theorem - by using the determinant as a endomorphism, then as $SL_n(\Bbb{R})$ is $1$ under the determinant, it is the kernel, and by FIT, the above is proved.  I was wondering how to prove this without the isomorphism theorem ? Importing DWG into QGIS project? I have a lot of DWG files like basemap, and water and wastewater network.  How do I import these files into my QGIS project? I am from a physics background and my mathematics is not very good, so pardon my insolence with the question.  Editing based on the comments : We know that $\pi$ in decimal (i.e. base 10) is transcendental. Is it possible to have a radix base in which $\pi$ can be rational in that base ?  PS : My question is in general for any transcendental number. nginx support for .htaccess / rewrite rules? Differences from Apache? I've been working with Apache http servers for quite some time, and finally making the move to static-content servers alongside the others dynamic-content machines.   I was wondering, does nginx support ".htaccess" files, and things like mod_rewrite?   As I'm very used to the syntax, I was wondering what the (syntax) differences were, and what the learning curve is like moving from Apache configs to nginx. Extract, convert, store and reuse (x,y) coordinate components How can I change a cell's background color based on the cell's current value? I have a column with function values of True or False:  =IF(ISNA(A1), false, true)   from row 1 to 5000+ rows. I would like to mark all the False as red background color or text as red. Is there any function available? How do you beta test an iphone app? How can you beta test an iPhone app?  I can get it on my own device, and anyone that gives me a device, I can run it on theirs, but is there a way to do a limited release via the app store for beta testing?  Related: Also, see  on getting your app onto phones without using the App Store. At what port did Lorance Effler born about 1787 in Germany come to the US? How many maximum CPUs does Ubuntu support by default? I think this is kernel dependent and probably will change over time depending on the kernel a release uses, correct me if wrong  I'd like to know two things for all the currently supported Ubuntu releases:  How many maximum CPUs can Ubuntu handle (by default) at the same time with a standard desktop kernel? Is that count different from a server kernel and 32bit/64bit systems?  Where can I find that information on my system? How do I enable Scroll Lock? Entering U.S. exactly on the day of visa "expiration date" I'm a bit surprised from my US Visa. I plan to go to a conference on 3rd of April. Amazingly though, the visa expiration date is written as April 3rd.  So what does that mean. Can I enter the US on April 3rd? or should I enter one day earlier? Using awk to sum the values of a column, based on the values of another column I am trying to sum certain numbers in a column using awk. I would like to sum just column 3 of the "smiths" to get a total of 212. I can sum the whole column using awk but not just the "smiths". I have:  awk 'BEGIN {FS = "|"} ; {sum+=$3} END {print sum}' filename.txt   Also I am using putty. Thank you for any help.  smiths|Login|2 olivert|Login|10 denniss|Payroll|100 smiths|Time|200 smiths|Logout|10 check if numbers from command line are powers of 2 My options to link large image into AI file My .psd file has a resolution of 6m x 3m @ 150 DPI. This makes it 35433px x 5906px in size. Photoshop CS6 saves the file as .tiff or .psb only. When I first import into Illustrator I get an error that the file is not readable but I have tried many options. Last one is not supported by AI.  So I'm puzzled... is there a way to link large images into Illustrator?