I found this question in Conway, and really have no idea how to answer it.  Can anyone provide any hints?     For each integer $n\geq 1$ determine all meromorphic functions on $\mathbb{C}$ $f$ and $g$ with poles at $\infty$ such that $f^n+g^n =1$.
Let $f$ and $g$ be entire functions such that $f^n+g^n=1$, where $n\geq 3$ is an integer. Prove that $f$ and $g$ are constant.  I suppose I should somehow prove that either $f$ or $g$ is bounded so that I can apply Liouville's Theorem, but I don't see how. I tried setting the derivative of the left hand side equal to zero and work with that but that did not seem to work.
I have an accompanied visa with my grandparents but because of some reason they cannot travel with me. I am above 17 years. Can I travel alone and will I be allowed to enter UK as my real aunt puts up there? Change edit approval threshold to (# approve − # reject ≥ N) Currently, the threshold for approving or rejecting a suggested edit is , whichever is reached first.  This means that, when  or just  edits get approved, it's often with a vote count of something like 1 reject / 2 approve (or 2 reject / 3 approve on SO).  Typically, these edits manage to get one or two very quick approve votes from, um, , after which it's very hard for the slower and more careful reviewers to accumulate enough votes to catch up before the edit is approved.  Conversely, when a valid edit gets wrongly rejected, this very rarely happens unanimously either.  More often, you'll see something like 3 votes to reject / 2 to approve, but that single last vote, no matter how well or poorly considered, is enough to tip the scales.  So I'd like to propose a simple change to the approval / rejection threshold:        Suggested edits should be approved when S = (# of approve votes &minus; # or reject votes) &ge; N, where N = 3 on SO and N = 2 on other sites.   Similarly, suggested edits should be rejected when S &le; &minus;N.      No, this change is not going to magically fix all the problems with suggested edit review.  But I believe that it would be a simple and conservative improvement over the current behavior:   For obviously good or bad edits that get approved / rejected unanimously, this suggestion would not change the current behavior in any way. For edits that get one mistaken or careless reject / approve vote (as happens pretty often), an extra approve / reject vote would be required to balance it.  This would slightly slow the review process for such edits, but not excessively so.  Further, I would argue that these are precisely the kind of edits that deserve that little bit of extra attention to make sure the eventual decision will be correct. Edits that are truly controversial, and for which the reviewer community is nearly exactly 50&ndash;50 split between voting to approve and reject, might stay in the review queue significantly longer (maybe twice as long on average) than under the current system.  However, this is a trade-off for the increased likelihood that the eventual decision will actually reflect the majority opinion among reviewers, rather than mere random chance.  In any case, even if reviewers are exactly 50&ndash;50 split, the  under the proposed scheme is only N&sup2;, i.e. 4 votes for other sites and 9 votes for SO.  Even a slight bias in the voting will further reduce this.  Besides, the longer the suggestion remains in the queue, the more likely it gets that someone will short-circuit the process by casting a binding vote (mod / post owner) or by choosing to improve the edit.     Ps. If it is felt that there's an issue with , a simple further chance to address that could be to make each reject vote count as, say, &minus;2 rather than just &minus;1 approval votes (and change the rejection threshold to S &le; &minus;2 &times; N to compensate).  This still wouldn't help with bad edits getting unanimously approved (which isn't really something that can be fixed, except maybe by slugster's cattle prod), but it would mean that each reject vote would now effectively cancel out two approve votes, titlting the balance for disputed edit suggestions in favor of rejection and making it easier for more careful reviewers to counter the "robo-approvers". Property of the conjugate transpose matrix with inner product Show that $11^{10} \equiv 1 (\mod 100)$ $11^{10} \equiv 1 \pmod{100}$  I tried to solve by using euler's theorem, But I got stuck.  $\gcd(11, 100) = 1$  $11^{φ(100)} \equiv 1 \pmod{100}$  $11^{40} \equiv 1 \pmod{100}$  I don't know how to go on as $11^{40}$ is bigger than $11^{10}$ How to let the user switch language in playframework 2 I'm using latex on a small netbook, and with average-sized files (~150 pages at the moment) compilation is already pretty slow. So I am looking for every way to speed up the compilation.  In this search, I found  explaining how to "precompile a preamble", or, latexically-speaking, how to make a custom format file. That works fine enough.  But my preamble isn't as static as it should be, I keep adding or modifying definitions in there. To mix the two solutions, at the moment, I use a Makefile together with latexmk, the makefile handling the regeneration of the .fmt file if needed, and latexmk taking good care of the rest.  But I have two problems with this :   integration with emacs to compile the whole document when working on a single file (make needs to be called in the proper directory) latexmk doesn't recompile the file every time the preamble is modified, because it doesn't count as a dependency.   So I'd like to find a way to get rid of this Makefile, and get all the stuff done by latexmk.  I edited my .latexmkrc to include this :     pdflatex = 'pdflatex -fmt main %O %S';  add_input_ext('pdflatex','fmt');  add_cus_dep('tex', 'fmt', 1, 'compilepreamble'); sub compilepreamble {     print "Preamble compiling...\n";     $command = '&amp;.pdflatex ./fmt/preamble.tex\dump';     system("pdflatex -ini -jobname='$_[0]' '$command'"); };      But with this, if the file main.fmt is not present or if fmt/preamble.tex is updated, the main.fmt file won't be regenerated. Actually, in the first case, I get an error from pdflatex saying the it can't find main.fmt format file. So I understand latexmk doesn't even try to build main.fmt, it's probably not a problem in my custom dependency. However, I think I've added everything necessary for this to work.  So... Did I forget something? Is there a way round? Or is it a hopeless quest? Package denyhosts in Ubuntu Trusty Tahr is deleted: temporary or forever? While doing a test-upgrade of our Ubuntu server to 14.04, I found that the package DenyHosts is no longer available. Installing it gives following error:  apt-get install denyhosts Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package denyhosts   Apparently it has been deleted, according to .  Will Denyhosts be available in the final release of Ubuntu 14.04? In "Seeing like a state" of James C.Scott there is a sentence at the beginning of a paragraph (Acknowledgements xi):     There are a good many scholars whose writings opened up new   perspectives for me or provided outstanding analyses of issues that I   could not have hoped to study so comprehensively on my own.   What worries me is a good many scholars. Is this some type of inversion or ancient English? Is this grammatically right? Why is a here? I thought that appropriate version would be There are many good scholars. Am I wrong? Story about a trip to a Valley of Sound Transferring through US airport. Do I need traveling visa? What is taking up so much space on my disk, beside the filesystem? I have only one disk in my computer, a 80 GB SSD. It is formatted as a single ext4 partition (no swap), and all the usual folders are installed on it (I keep lots of data on external media, but /home and all the rest is on the SSD).   Today I booted it and I got a message that the drive is full. I opened Disk Usage Analyzer to look at what takes up space. It insists that 67.8 GB of the disk are used, and that / is taking up 36.4 GB. Which leads to the question, where are the missing 30 GB, if not on the file system?!    Just to have a comparison, I added up all the sizes of all readable folders listed in Nautilus as subfolders of / (including the hidden ones). I got 20.9 GB. Trash was unreadable, but I know it has 16.2 GB, so the sum is 36.1 GB, around the same as what Disk Usage Analyzer is reporting. There were some system folders which were unreadable, like proc, but I doubt that they add up to 30 GB - else it wouldn't be possible to install Ubuntu on small disks, and I've seen it run on 2.5 GB. I think they must be the 0.3 GB difference between my calculation and the Disk Usage Analyzer's report.   So I'd like to know, what is eating up these 30 GB and how do I get it to free them?     Edit with answers to CYREX's questions   Booted from Ubuntu 10.10 64-bit live CD (same as my system).  fsck result:   root@ubuntu:~# fsck /dev/sda1 fsck from util-linux-ng 2.17.2 e2fsck 1.41.12 (17-May-2010) /dev/sda1: clean, 265956/4890624 files, 18073343/19537408 blocks  Booted from the SSD. Emptied the trash, and the 16 GB from there are now free. The 30 GB are still missing.    I'm not experienced enough to know what counts as weird in a log. Here are my messages log and my syslog since last boot. Maybe you can find something in them:       Here it got really strange. I plugged in an external 500 GB HDD. Disk Usage Analyzer overreported the available space, then showed space missing (76 GB used, but only 24 in folders).      Booted again from the LiveCD, started the Disk Usage Analyzer from it and got the same results as from the installed Ubuntu, within 1-2 GB.   Edit with answer to CodeMonk:  That would have been a nice solution, but the partition is really 80 GB - I mean 74 GB + marketing "error", anyway the whole disk is formatted. It also shows that over 50 GB are used, so where are the 30 GB if not in files and folders?    GParted also reports the correct size of the external HDD. What is the best way to generate a GUID/UUID from Apex code (such as a trigger)? Preferably in the following format:     nnnnnnnn-nnnn-nnnn-nnnnnnnnnnnnnnnnn   Example:     13219ec0-3a81-44c5-a300-de14b7d0235f What we've gelost — why doesn't English use the prefix "ge-"? The Germanic languages that I'm familiar with all use a prefix similar to ge- on past participles:  German: Ich habe mir den Fuß gebrochen. Dutch: Ik heb mijn voet gebroken.  But English doesn't do this at all:  English: I've broken my foot.  Where did this prefix come from? Did English ever have the ge- past participle prefix? If so, why was it lost? How do I straighten UV maps? How to remove/install a package that is not fully installed? Improving Review Queues - Design overview II: Changing review bans and other new features My question relates to Chapter 3, Exercise 8 in &quot;Baby Rudin&quot;. It states: If $\sum_n a_n$ converges, and if $\{b_n\}$ is monotonic and bounded, prove that $\sum_n a_n b_n$ converges. My attempt would have been: Since $\{b_n\}$ is monotonic and bounded, $\{b_n\}$ converges and it exists $\inf \{b_n\}$ as well as $\sup \{b_n\}$. But then we have $$ \left| \sum_n a_n \inf \{b_n\} \right| \leq \left| \sum_n a_n b_n \right| \leq  \left| \sum_n a_n \sup \{b_n\} \right| \leq \max \left( \left| \sup \{b_n\} \right|, \left| \inf \{b_n \} \right| \right)\varepsilon \leq \tilde{\varepsilon} $$ since $\sum_n a_n$ converges and $\max \left( \left| \sup \{b_n\} \right|, \left| \inf \{b_n \} \right| \right)$ is a finite number. This would imply, by the comparison test, that $\sum_n a_n b_n$ converges as well. $\quad \Box$ But as there was a way longer, more rigorous proof chosen in this , I'm a bit suspicious that my proof is not complete. Am I missing something?  EDIT: Thanks everyone! @hermes: The last part of your proof gave me the following idea. As $\lim_{n \to \infty} b_n = c$ and $\{b_n\}$ is monotonic, couldn't we just set $b_n = c - c_n$ with a monotonically decreasing sequence $\{c_n\}$ which has $\lim_{n \to \infty} c_n = 0$. Then we have $$\sum_n a_n b_n = \underbrace{c \sum_n a_n}_{\text{converges by assumption}} - \underbrace{\sum_n a_n c_n}_{\text{converges by Theorem 3.42}} \leq \varepsilon_1 - \varepsilon_2 = \varepsilon $$ since  Theorem 3.42 Suppose  the partial sums of $\sum_n a_n$ form a bounded space $\quad \checkmark$ $c_0 \geq c_1 \geq c_2 \geq \dots \quad \checkmark$ $\lim_{n \to \infty} c_n = 0 \quad \checkmark$  Then $\sum_n a_n c_n$ converges.  Thus $\sum_n a_n b_n$ converges as well. $\quad \Box$ Now that should hold, I think. So I wouldn't need to go through all the estimates. Display top tags & percentiles from additional Stack Exchange sites on Careers Are the "top tags &amp; percentiles" from Stack Exchange sites other than Stack Overflow displayed in the Careers site?  If not can they be added?  If they are, then what are the requirements for them being displayed in the Careers site? is the group of rational numbers the fundamental group of some space? unsigned int vs. size_t I notice that modern C and C++ code seems to use size_t instead of int/unsigned int pretty much everywhere - from parameters for C string functions to the STL.  I am curious as to the reason for this and the benefits it brings.