Building and Running my First App
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Find all n such that $\phi(n) = n/2$ My idea for the solution is something like this:  Since $2 | n$, $n = 2^a p_1^{e1} p_2^{e2} \cdots p_t^{et}$ where $a \geq 1$.  Then, $n/2 = \phi(2^a) \phi(p_1^{e1}) \phi(p_2^{e2}) \cdots \phi(p_t^{et})$.  Looking at the case that $t = 0$,  $n/2 = \phi(2^a) = 2^{a-1}$, and therefore $n = 2^a$.  Otherwise, $n = 2^a \phi(p_1^{e1}) \phi(p_2^{e2}) \cdots \phi(p_t^{et}) = n = 2^a p_1^{e1} p_2^{e2} \cdots p_t^{et}$. Since $\phi(n) &lt; n$, this is a contradiction, and therefore, the only $n$'s that apply are the powers of 2.  Is this right? Also, we were asked to find $n$ such that $\phi(n) = n/3$. How would I go about that one? Newton's Law of Graviation: Why $G$ and not e.g. $\dfrac{1}{4\pi G_0}$? Taking a spin off of this question:  in a new direction for 2014.  Taking into account a basic Windows infrastructure:   domain controllers Exchange 2007/2010/2013 Sharepoint SQL File Servers / Print Servers AD Integrated DNS AD authenticated 3rd party devices (let's say 802.1X for networking and maybe some content-filtering, etc.) AD/LDAP authenticated "administrative" functions on IT apps/hardware/etc. perhaps some KMS stuff throw in a CA if you'd like home grown apps 3rd party in-house apps   Now, let's rip it all out and decide we are going to the cloud.  We've contracted to move Exchange/Sharepoint/File Services to Office 365.  SQL will now be hosted as well on  something like Azure.  We've gotten away from the need for AD-DNS and simply run everything via a simple Windows DNS server.  We still need 802.1X and would like SSO if possible to our various cloud apps.  Home grown and 3rd party in-house apps would likely stay, but have the ability to use internal user databases instead of AD authentication  The question is...do we really need Active Directory at all?  Or more to the point, AD on-premise or even hosted via Azure or similar (ADFS) or running ADDS on a hosted VM through Azure or similar.  Could/Should we look to something else like a 3rd party SSO option such as  or similar that can provide SSO functionality even if it is as simple as LastPass or similar for each user?  What kind of legitimate needs does AD fulfill if everything else in the cloud?  Could a MS-centric infrastructure get away with not having AD at all if they move everything that previously relied on AD to SaaS offerings that didn't rely on AD authentication? Is it safe to travel to Miami Beach shortly after hurricane Irma? Two months ago my girl and I booked our vacation. We are from Berlin, Germany and wanted to see the U.S. Our first stop is Miami Beach at the 15th and we want to stay there for 3 days and continue to NYC. Later on we will go to Vegas and come back to Miami the 26th of September and stay there another 4 nights.  I expect the hurricane will be gone by the 15th, but I have no idea whether it will be okay. For me okay means that we can reach our hotel and sleep there.  What do you suggest? I know this question is primarily opinion based, but here in Germany we don't have hurricanes and I don't know how fast the state will recover. Are "white" and "black" ever capitalized when referring to people? Login SSH with .ppk file on Ubuntu Terminal I have a production server. To login to the server I must use a .ppk file.  How to login with Ubuntu Terminal and .ppk file?  I tried this :  ssh -i location/file.ppk username@server-ip   but it is showing an error message. Show that $\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$ Prove that:  $$\lim_{n\to\infty} \sqrt[n]{a^{n} + b^{n}} = \max(a, b)$$  I don't have a clue even how to start the proof here. Any hint is appreciated! How to use Class in Java? There's a good discussion of Generics and what they really do behind the scenes over at , so we all know that Vector&lt;int[]&gt; is a vector of integer arrays, and HashTable&lt;String, Person&gt; is a table of whose keys are strings and values Persons.  However, what stumps me is the usage of Class&lt;&gt;.  The java class Class is supposed to also take a template name, (or so I'm being told by the yellow underline in eclipse).  I don't understand what I should put in there.  The whole point of the Class object is when you don't fully have the information about an object, for reflection and such.  Why does it make me specify which class the Class object will hold?  I clearly don't know, or I wouldn't be using the Class object, I would use the specific one. Find expected value of $\frac{1}{1+\xi}$ Find expected value of $\frac{1}{1+\xi}$ if $\xi$ has Poisson distribution.  My try:  $$E\left[ \frac{1}{1+\xi}\right]=\sum_{k=0}^{\infty}{x}_{k}{p}_{k}=\sum_{k=0}^{\infty}\frac{1}{k+1}\frac{\lambda^ke^{-\lambda}}{k!}$$  Is it right? I'm making a trip back home (to the coast) shortly, and I would like to bring back sand from the beach with me as a keepsake or memento. It's just a short weekend trip, and I won't be checking any luggage, so I was wondering if it's even worth bothering trying to bring sand aboard the plane in my carry-on?  If so, what can I do to make the security screening as smooth as possible? I was planning on putting the sand in sandwich-sized plastic bags, enclosed in a larger quart- or gallon-sized bag. JavaScript OR (||) variable assignment explanation Addons: Only some .zips will install Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password? How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$? We are asked the following:      let $f(x)$ be a continuous function on $[0, 1]$ such that   $$\int _ {0} ^ {1} \ f(y) dy = 1$$   prove that $f(x) = 1$ for some $x ∈ [0, 1]$   The question asks to take into account Rolle's Theorem and Mean Value Theorem.  I'm aware of the definitions, but I am really unsure how to answer this question and my tutors are not really responding till after easter.    Could someone please help? Why is there a "y" involved?  Thanks you Tail sum for expectation In , the tail sum formula for expectation is introduced for a nonnegative (0,1,...) discrete random variable $X$:  $$E(X) = \sum_{i=0}^\infty P(X &gt; i).$$   I wonder if there is a similar formula for nonnegative continuous random variable $X$:  $$E(X) = \int_0^\infty P(X &gt; x) dx?$$  If no, are there some conditions for it to hold? And how can it be proved?  Here is my thought:  If the cdf $F$ of $X$ is bijective, then $X=F^{-1}(U)$ for some random variable $U$ uniformly distributed over $[0,1)$. So $$E(X) =     \int_0^1 F^{-1}(u) du.$$  To prove the tail sum formula, it suffices to prove $$\int_0^1     F^{-1}(u) du = \int_0^\infty P(X &gt; x) dx.$$ But I am stuck here.   What's more, is the condition that the cdf $F$ of $X$ is bijective really necessary for tail sum formula to hold? Can tail sum formula be generalized to a random variable that is not necessarily nonnegative?   Thanks! Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$ Show that    $$1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$$   So, I use Fermat's little theorem, that is if $p$ does not divide $a$, then $a^{p-1}$ is congruent to $1$ (mod $p$). But I'm still confused. If $1^{p-1}$ is congruent to $1$ (mod $p$), $2^{p-1}$ is congruent to $1$ (mod $p$), and $p$ does not divide $p-1$, so $(p-1)^{p-1}$ is congruent to $1$ (mod $p$). How does that equal $-1$ (mod $p$)? I have removed Windows 7 using GParted, and want my computer to boot straight into Ubuntu, but I still get the dual boot screen, how can I fix this? After a very long time will we see more stars (due to the fact that more light is get to us) or less stars (as the universe expends and light have to pass larger distance)? In general, can stellar objects go outside of the scope of the observable universe or is it only growing with time? Calculations are always better than just discussion. Does it have any connection to dark matter? Round a double to 2 decimal places I've lost my portal home, and I am invincible. How can I leave the nether?