Does $f(\bar{z}) = \overline{f(z)}$ generally?
Holomorphic functions: is it true that $f(\bar{z})=\overline {f(z)}$?
Binomial Distribution Problem - Airline Overbooking During the last phase of layout I frequently get a single line or two on a separate page. Rather then pulling the whole paragraph on that last page I would like to "squeeze" the lines on the previous page a bit.  Is there a way to mark the current page to be squeezed a bit if necessary, but let LaTeX reset this marking automatically after the page is done? If $a^{n}-1$ is prime then $a=2$ and $n$ is prime? I was doing some basic Number Theory problems and came across this problem :     Show that if $a$ and $n$ are positive integers with $n\gt 1$ and $a^{n} - 1$ is prime, then $a = 2$ and $n$ is prime   My Solution : (Sloppy)        $a^{n}-1$ = $(a-1)$ . $(a^{n-1} + a^{n-2} + ... + a + 1)$   This means that $(a-1)$ | $(a^{n}-1)$    But $(a^{n}-1)$ is prime   So , $(a-1)$ = 1 $\Rightarrow$ $a = 2$   Now , let $n$ be composite   $n = kl$ , where $1 \lt k \lt n$ and $1 \lt l \lt n$   Now , $a^{kl}-1$ = $(a^{k}-1)$ . $(a^{k.{(l-1)}} + a^{k.{(l-2)}} + ... + a^k + 1)$   This means that $2^{n} -1$ is composite    Hence , we have achieved a contradiction      My Question : Am I correct ? Computer keeps restarting by itself Converting Polygon into single or all Points using QGIS? Sometimes, I want to have enumerate lists in LaTeX start at other than the first value (1, a, i, etc.) How can I make an enumerate list start at an arbitrary value? Is there a mass spectrometer software that can measure the mass of a proton Incoming light reacts with the several types of cone cells in the eye. In humans, there are three types of cones sensitive to three different spectra, resulting in trichromatic color vision. Each individual cone contains pigments composed of opsin apoprotein, which is covalently linked to either 11-cis-hydroretinal or more rarely 11-cis-dehydroretina.  The opsins (photopigments) present in the L and M cones are encoded on the X chromosome.  A very small percentage of women may have an extra type of color receptor because they have different alleles for the gene for the L opsin on each X chromosome. X chromosome inactivation means that only one opsin is expressed in each cone cell, and some women may therefore show a degree of tetrachromatic color vision. Tetrachromacy is also demonstrated among several species of birds, fish, amphibians, reptiles and insects.  Humans cannot see ultraviolet light directly because the lens of the eye blocks most light in the wavelength range of 300–400 nm.  So, besides above mentioned exceptions, is it possible due to mutations or genetic engineering to see UV or infrared. What kind of mutations should be made or are the changes to be made in the opsines to big to create 'alien' eyes? Replicate data from one list to another list sharepoint I have a list A with columns Emp ID, First name &amp; last name and list B wih column name Emp ID, First name, last name , phone number and address.  I want functionality such that when i enter item in List A and save same data should get copied in 3 columns of list B. Can someone help me with the approach. Thnks I have 28,000 files of size 6.7 GB in the directory aaa/input. I need create TAR files in the directory aaa/output, such that each TAR file cannot exceed 1.9 GB, so I have to tar the 28,000 files into 4 TAR files (6.7/1.9) as Log_(current date)_01.tar Log_(current date)_02.tar ... etc.  such that each tarball is less than 1.9 GB. Is there a way to do this using a Unix script? Why couldn't the Jedi detect Senator Palpatine as having powers? In Return of the Jedi, when trying to sneak into the base on a shuttle, Luke said he senses Darth Vader's presence and said he shouldn't have come lest he jeopardize the mission. Darth Vader also sensed Luke, but let him in anyways. Also, Yoda and Obi-Wan could detect the Force in young Anakin.  So if Jedi and Sith can detect each other, why couldn't they detect Senator Palpatine to begin with? It seems like a giant plot hole. Is there any module or some configuration that I can define the meta tags for the views page display in drupal 7 using  3.0? There is some behavior I can't understand in the Unity Desktop.   Open nautilus via. clicking in the launcher onto the home-button Navigate to for example the windows-partition in nautilus Minimize nautilus Click on nautilus in the launcher doesn't open the nautilus with windows-partition, instead it opens a new window with the home folder.   Is there a workaround for this strange behavior?  Regards, Arthur Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$ Prove that (a) gcd(a, b) = gcd (a, b – a) (b) Let r be the remainder if we divide b by a. Then gcd(a, b) = gcd(a, r).  I solved part a like: Assume a=pcommonpa b=pcommonpb gcd (a,b) = pcommon b-a = pcommon*(pb-pa)  So: gcd(a, b-a) = common again But I need help for part b guys I can solve it but I need a mathematical expression. When umpire change the cricket ball, was the old ball thrown as waste or keep for reuse? Should we write “allow” or ”allows” in “require that the class allow[s]”? Can you explain to me whether I should or should not use ‑s at the end of the  verb allow in this sentence?     This function requires that the container class allow[s] random access   The sentence in the book I read wrote allow without ‑s. However, the container class is a third-person singular, so the ‑s must be required. Is that right? How to turn off "unread messages" feature on Windows XP login screen? In Windows XP, if you have logged onto Windows Live Messenger at some point, then it'll start displaying how many unread messages on the Windows login screen. How can I turn it off? I have a Storex eZee Tab 702 tablet. My Google Play Store was working very well until a few weeks ago, when it started saying,     Error while retrieving information from server [DF-DFERH-01]   I tried to clear the cache, clear the data, force stop, and downloading another Google Play Store, but I'm still having the same problem.  How can I fix this issue? Convergence of the series $ \sum_{n=1}^{+ \infty } \frac{1}{n \cdot \ln(n) \cdot (\ln(\ln(n)))^{a}} $ I have a problem with a convergence of the series $ \sum_{n=1}^{+ \infty } \frac{1}{n \cdot \ln(n) \cdot (\ln(\ln(n)))^{a}}$ depending on the parameter $a$. I know that  $\frac{1}{n} \rightarrow 0$, $\frac{1}{\ln(n)} \rightarrow 0$, but I don't know how to deal with $\frac{1}{\ln(\ln(n)))^{a}}$ and how to get to the final answer. So far I solved tasks with  $\frac{1}{n ^{a}}$ and I know that $a&gt;1  \Leftrightarrow \sum_{n=1}^{+ \infty }\frac{1}{n ^{a}}$ is convergent, but in this task I cannot use it. Can you help me? I'm trying to install KDE 5 on my Ubuntu 16.04 system as per the instructions in , but I'm getting the below error message when running sudo apt-get install kubuntu-desktop.  Is there something I can do to resolve this?  Need to get 682 kB/326 MB of archives. After this operation, 1,272 MB of additional disk space will be used. Do you want to continue? [Y/n] y Err:1 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              gtk2-engines-oxygen amd64 1.4.6-1ubuntu1   Temporary failure resolving 'ir.archive.ubuntu.com' Get:2 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libkf5sendlater5 amd64 4:15.12.3-0ubuntu1 [45.2 kB] Get:3 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libthreadweaver4 amd64 4:4.14.16-0ubuntu3 [46.6 kB] Get:4 http://ir.archive.ubuntu.com/ubuntu xenial/universe amd64              libfarstream-0.2-5 amd64 0.2.7-0ubuntu1 [192 kB] Fetched 284 kB in 1min 9s (4,093 B/s)         E: Failed to fetch http://ir.archive.ubuntu.com/ubuntu/pool/universe/g/             gtk2-engines-oxygen/gtk2-engines-oxygen_1.4.6-1ubuntu1_amd64.deb               Temporary failure resolving 'ir.archive.ubuntu.com'  E: Unable to fetch some archives, maybe run apt-get update or              try with --fix-missing?