If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$. Also... $a,b$ and $n$ are natural numbers.  I feel I should begin with EEA to multiply out the gcd's, but I don't know where to go from there...
Let $a,b,n$ be integers such that  $\gcd(a,n)=\gcd(b,n)=1$. How to show that $\gcd(ab,n)=1$?   In other words, how to show that if two integers $a$ and $b$ each have no non-trivial common divisor with and integer $n$, then their product does no have a non-trivial common divisor with $n$ either.     This is a problem that is an exercise in my course.   Intuitively it seems plausible and it is easy to check in specific cases but how to  give an actual proof is not obvious.
How to automount a partition on login? I have my musics in another partition of the HD, and I would like that, on login, the partition to be auto-mounted, so I can just open the media player and listen to my music. Is there a way? How to search inside files on Windows 7? In Windows XP we can search for files that contain a defined keyword (inside all files types).  Windows 7 can look inside files for a keyword, but only for text files. (*.doc, *.txt, *.inf, ...), not (*.conf, *.dat, *.*, ...).   don't contain any filter I can use for this.  How is this possible? Changing threshold in logistic regression Suppose that you have a logistic model and the predicted probabilities of a $1$ all are in $[0.2,0.3]$. So the predictions would be "0" based on a threshold of $0.5$. What would be a good threshold to choose? Short story with aliens who hear their own thoughts as god-like voices I would have read this about 20-25 years ago.  I believe the subject was an alien individual, but it could have been a non-standard human instead.  The hook of the story was that the subject lacked an organ like the  that allows the halves of the brain to communicate efficiently, allowing the illusion of a single consciousness.  The subject is conscious, and has thoughts, but is subject to hearing commands like "Wash your hands!" "Fetch water!" within its head.  I recall the subject (and others like the subject) believing that the voices are their gods talking to them.  To the reader it becomes clear that this is a separate part of the subject's own mind that is responsible for long-term planning and simply can't communicate with the rest of the mind in the way a "normal" human is accustomed to. I have been facing hard time understanding meaning of "random sample" as well as "iid random variable". I tried to find out the meaning from several sources, but just got more and more confused. I am posting here what I tried and got to know:  Degroot's Probability &amp; Statistics says:     Random Samples / i.i.d. / Sample Size : Consider a given probability distribution on the real line that can be represented by either a p.f. or a p.d.f. $f$. It is said that $n$ random variables $X_1 , . . . , X_n$ form a random sample from this distribution if these random variables are independent and the marginal p.f. or p.d.f. of each of them is $f$. Such random variables are also said to be independent and identically distributed, abbreviated i.i.d. We refer to the number n of random variables as the sample size.   But one of the other statistics book I have says:       In a Random Sampling, we guarantee that every individual unit in the population gets an equal chance(probability) of being selected.   So, I have a feeling that i.i.d.s are elements that construct random sample, and the procedure to have random sample is random sampling. Am I right?   P.S.: I am very confused about this topic, so I will appreciate elaborate reply. Thanks. In "Winnie the Pooh", Why isn't the Hundred Acre Wood  plural? When I read some of these Winnie the Pooh stories to my kids at night, the place where the story takes place is the Hundred Acre Wood, not Hundred Acre Woods.  Why is that? Replace unknown reference (?) with the tag from \ref or \cite I'm new with LaTeX and I'm trying to make a table with the elements centered vertically and horizontally. I've searched for this question, it seems like most people were trying to do things a little more complicated than this, resulting in complicated answers I couldn't understand. The table below is already centered horizontally, but the elements are aligned to the top of the cells instead of the center. How do I fix this?      \begin{tabular}{*{5}{|c}|}         \hline         $p$ &amp; $q$ &amp; $p \land q$ &amp; $p \lor q$ &amp; $p \to q$\\         \hline         T &amp; T &amp; T &amp; T &amp; T\\         \hline         T &amp; F &amp; F &amp; T &amp; F\\         \hline         F &amp; T &amp; F &amp; T &amp; T\\         \hline         F &amp; F &amp; F &amp; F &amp; T\\         \hline     \end{tabular} Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues. Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.   We assume there exist $k$ incongruent quadratic residues and each yield two solutions of the equation $x^2 \equiv a (\mod p)$. Also each of these solutions are incongruent, right ? So we have $2k$ solutions to quadratic congruences.  Then there are $p-1$ squares of the least residues, $1$ through $p-1$. But these need not be incongruent (consider $p = 7$ and $1^2, 6^2$). Then $2k = p-1$, why ?  Could someone explain to me in details what the reasoning is ? Why should users have to press Return twice to insert new lines? When I post a question and want to add a new line, I have to press Return two times, or else the next text will appear on the same line.  Is this really supposed to behave this way? If so, why? headed or heading, started or starting? Consider:  Two units are headed your way. Two units are heading your way. Don't get me started! Don't get me starting!  Is there any difference in meaning? And I don't see why passive voice is used here. I would think they have similar meaning here. Help me to clarify! I just updated my Moto X to latest and greatest Android 4.4 KitKat (I even did full factory reset just to be sure) and now I'm trying to install  but unable to do so, I'm getting following error:     Unknown error code during application install "-24"   Please advise. I have a problem with the interpretation of a test result in which the p-value is 8.6e-28. How should it be interpreted? What is the e for?  Specifically, I used White's Test for the homoscedasticity assumption of a linear regression:  White's general test statistic :  150.0535  Chi-sq( 9)  P-value =  8.6e-28 In MTG, what happens when a player loses in multiplayer? magit: how to diff the same file between two different commits on the same branch? This is a  about IPv6 Subnetting.      Related:               I know a lot about , and as I prepare to (deploy|work on) an IPv6 network I need to know how much of this knowledge is transferable and what I still need to learn. IPv6 seems at first glance to be much more complex than IPv4. So I would like to know:   IPv6 is 128 bits, so why is /64 the smallest recommended subnet for hosts? Related to this:   Why is it recommended to use /127 for point to point links between routers, and why was it recommended against in the past? Should I change existing router links to use /127? Why would virtual machines be provisioned with less than a /64 worth of addresses? Are there other situations in which I would use a subnet smaller than /64?  Can I map directly from IPv4 subnets to IPv6 subnets? For instance, does an IPv4 /24 correspond directly to an IPv6 /56 or /120? My interfaces have several IPv6 addresses. Must the subnet be the same for all of them? Why do I sometimes see a % rather than a / in an IPv6 address and what does it mean? Am I wasting too many subnets? Aren't we just going to run out again? In what other major ways is IPv6 subnetting different from IPv4 subnetting? Replace a xtick by a letter in Tikz Bolding with ** isn't working properly Have a look at   One of the bolds works, and the other one just turns up as ** in the actual post.  This is the string that isn't working: **x**ml n**ib**  Which renders as: xml nib How do I use regular expressions in bash scripts? I want to check if a variable has a valid year using a regular expression. Reading the  I understand I could use the operator =~  Looking at the example below, I would expect to see "not OK" but I see "OK". What am I doing wrong?  i="test" if [ $i=~"200[78]" ] then   echo "OK" else   echo "not OK" fi I often find myself wishing SO supported drag and drop. For example I drag a tag to my favs and it would add it, or when searching by tag I would like to drag the tag to the search box and get [asp.net] added in the search box.   Does it make sense to add this feature or is it just too much work for so little use?