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$x^a - 1$ divides $x^b - 1$ if and only if $a$ divides $b$ Let $x &gt; 1$ and $a$, $b$ be positive integers. I know that $a$ divides $b$ implies that $x^a - 1$ divides $x^b - 1$. If $b = qa$, then  $$x^b - 1 = (x^a)^q - 1^q = (x^a - 1)((x^a)^{q-1} + \ldots + x^a + 1).$$  I'm interested in the converse of the statement. If $x^a - 1$ divides $x^b - 1$, does this imply that $a$ divides $b$? Find $\int \frac{x^3}{x^2-1} \:\mathrm{d}x$ Find $\displaystyle \int \dfrac{x^3}{x^2-1} \:\mathrm{d}x$.   I think there are a few ways to do this. We could just break this up using long division or break it up into partial fractions then use long division. My homework says to break this up into its roots so that's why I brought up partial fractions. Is that the best way to do it here? I have updated from Windows 7 Ultimate x64 to Windows 10 Pro x64 using Media Creation Tool.  After some weeks when I'm clicking on the start button nothing happens and the whole status bar becomes unresponsive. After trying to restart explorer.exe from Task Manager explorer.exe fails to initialize. It just shows the start button, Cortana and the search bar, TaskViewer (if that's how it is called) and the Action Centre button.  Any ideas?  I tried running:   sfc /scannow and no errors were found chkdsk /f and no errors were found   A full system restart seems to do the trick but after some time like a few hours it stops responding again.  My configuration:   CPU is Intel i5 4690K OC-d to 4.5Ghz GPU is AMD Radeon HD 7750 Saphire 1Gb GDDR5 Edition   EDIT: After some GOOGLE SEARCHING if i try to run from Task Manager C:\Windows i can actually open a window. The start bar isn't responding though and there are still no desktop icons or wallpaper. Does iOS 7 cellular tethering limit the number of WiFi clients? I'm looking on Apple's site and can't find any published limits on how many clients can connect to one iPhone / iPad with cellular tethering enabled in the US.  Setting aside the obvious limit where 1,000 devices would overwhelm the data connection in practice if they all want data at the same time, is there a hardware or software limit of perhaps 5 or 10 devices that can connect to one device over WiFi? When editing a question on , I observed that a link which was not rendered in the post was hyperlinked in the edit preview (see pictures below). I tried reproducing it in the  to see if this also happens when the post is posted for the first time and observed the same. It seems to be a bug after the shift to CommonMark, leading to the different rendering of links on client and server-side. A link following a special character (without any space) is not hyperlinked in the post but is hyperlinked in the preview. A link separated from the special character with a white space appears to have no such problem. (see pictures below and my ). Link not hyperlinked in post  Same link hyperlinked in preview What are drawbacks or disadvantages of singleton pattern? The  is a fully paid up member of the 's , but it lately seems rather orphaned by the developer world. I still use quite a lot of singletons, especially for , and while you have to be a bit careful about multithreading issues (like any class actually), I fail to see why they are so awful.  Stack Overflow especially seems to assume that everyone agrees that Singletons are evil. Why?  Please support your answers with "facts, references, or specific expertise" Minecraft pocket edition restoring skin problem I updated Minecraft PE so I can have custom skins. I clicked on 'restore skins' without selecting any particular skin, It is now stuck with a  message saying 'we're restoring your skins!' but it has been like that for 20 minutes. Is there a reason why it is like this? Using package nomencl How do I properly access Windows software RAID 0? I am a new Ubuntu user with a fresh installation, and am eager to get started with it. However, all of my important data is on Windows software RAID 0 array, and I need it to stay there as I'm also dual booting Windows. I need access to this data on Ubuntu, and can't really get anything real done until I have access.  I have already researched this subject as best as I could, and I managed to find a very helpful post:      The post describes how to get Ubuntu to see a Windows RAID 0 array that is made up of two drives. The main command used is sudo mdadm --build /dev/md0 --chunk=64 --level=0 --raid-devices=2 /dev/sdd2 /dev/sdc2. According to that user, and the other posters in the thread, it actually does work. That's great.  I have not tried following these instructions yet. Why? The post includes a warning about how you must not write to it if you enter the wrong chunk size; it's understandable how that could cause problems. My concern is that my setup is different to their example, and I am not sure that the commands should be entered exactly the same for my setup. I am afraid to break it by doing it wrong, and therefore wish to get the advice of somebody more experienced.  This is how my setup differs from their example:   I have three 1 TB drives, not two drives (of whatever size they used). I have two RAID 0 partitions spread across those three drives: one 500 GB and 2.3 TB. This means that I need to NOT use the full disks when creating the RAID array, but instead use just part of them. I used a non-default block size for at least one of my RAID 0 partitions when I set them up years ago. I have no idea if this block size is the same as the chunk size that they mention. My 500 GB partition has a block size of 4 kb (4096 bytes per cluster), and my 2.3 TB partition has a block size of 64 kb (65536 bytes per cluster).   The relevant output from sudo lsblk -o NAME,FSTYPE,SIZE,MOUNTPOINT,LABEL (for just those three RAID0 drives) is:  NAME   FSTYPE   SIZE MOUNTPOINT            LABEL sdb           931.5G             ├─sdb1            1M             ├─sdb2          127M             └─sdb3        931.4G             sdc           931.5G             ├─sdc1            1M             ├─sdc2          127M             └─sdc3        931.4G             sdd           931.5G             ├─sdd1        166.7G             └─sdd2        764.7G    The relevant output from cat /proc/partitions (for just those three RAID0 drives) is:  8       16  976762584 sdb 8       17       1024 sdb1 8       18     130048 sdb2 8       19  976631478 sdb3 8       32  976762584 sdc 8       33       1024 sdc1 8       34     130048 sdc2 8       35  976631478 sdc3 8       48  976762584 sdd 8       49  174763008 sdd1 8       50  801865728 sdd2   The "Disks" program in Ubuntu displays the following partitions for my drives:  /dev/sdb:   GUID Partition Table . /dev/sdb1:  1.0 MB, Microsoft LDM metadata. /dev/sdb2:  133 MB, Microsoft Reserved. /dev/sdb3:  1.0 TB, Microsoft LDM data. /dev/sdc:   GUID Partition Table partitioning. /dev/sdc1:  1.0 MB, Microsoft LDM metadata. /dev/sdc2:  133 MB, Microsoft Reserved. /dev/sdc3:  1.0 TB, Microsoft LDM data. /dev/sdd:   Master Boot Record partitioning. /dev/sdd1:  179 GB, Unknown. /dev/sdd2:  821 GB, Unknown. /dev/sdd:   136 MB, Unallocated space.   I hope I've provided enough information here. So now, my question is this: what is the proper command for me to enter with my setup, so that I can access both of my Windows RAID 0 partitions from Ubuntu?  Thank you very much in advance. Is every metric space a subspace of some connected metric space? Is every metric space a subspace of some connected metric space? If the space itself is connected then we're done, but if not then I think we can extend our metric space to make it connected.  I'm not sure whether this will work or not, but intuitively I think the answer is yes. Login failed for user - Error 18456 - Severity 14, State 38 How can be solved the equation $x^3+x-1=y^2$ in positive integers?    I know this equation defines an elliptic curve, but this seems to be a non-elementary way to solve this question. Is there a more elementary solution?   By the way I found three solutions: $(1,1), (2,3)$ and $(13,47)$. Is this related to the law group property of elliptic curves? Thanks for further answers. Is there a number whose absolute value is negative? Lost/Deleted dpkg (package manager for Debian). How do I get it back? OS: Ubuntu 12.04  Accidentally deleted dpkg. Now, packages can't be installed. So, needs an dpkg installer which installs packages. $\frac{1}{99989999} = 1.00010002000300050008001300210034005500890144... \times 10^{-8}$    (), which includes the Fibonacci sequence $(1\ 1\ 2\ 3\ 5\ 8\ 13\ 21\ 55\ 89\ 144\ldots )$.  This is fascinating to me but I can't figure out how this works, and a Google search doesn't seem to reveal anything. As far as I understand, one of the main claimed problems with initializing e.g. a feed-forward neural network (with several $\text{tanh}$ or $\text{ReLU}$ layers) with $W=0$ is that it doesn't break "network symmetry", meaning, backpropagation would propagate the same error through all such units (i.e. "nudging all weights in the same direction"). This is, I presume, undesirable because we would not be learning "different" calculations through different paths of the network.  However, I'm confused why that even matters in this case given the fact that if $W$ ever drops to 0, we will effectively be propagating no gradients at all through the network, since W=0 would multiply all errors from the output and prevent any learning.  Put another way, even if $W=0$ does not break network symmetry (wasting calculations and paths in the network) is it correct to say that if $W=0$ (e.g. by initialization) we are effectively killing gradients in a neural network, and thus no learning can take place? I have to move a MongoDB Collection (Size: 1TB+) from Sharded MongoDB Cluster to another[5 shards on both clusters]. During this operation, it is assumed that the accompanying program will be offline, so no need to worry about inconsistent data, but I need to minimize the downtime.  I've tried testing it with mongodump and mongorestore, but looks like that is taking ages to finish.  Please share your experiences for such kind of scenarios.  Note: Cluster has only one collection, so I am open at cluster level sync as well. I'm working in C, and I have to concatenate a few things.  Right now I have this:  message = strcat("TEXT ", var);  message2 = strcat(strcat("TEXT ", foo), strcat(" TEXT ", bar));   Now if you have experience in C I'm sure you realize that this gives you a segmentation fault when you try to run it. So how do I work around that? found a 1994 uncashed profit sharing retirement plan check I found an old un-cashed check dated 1994 for $487 from my Xerox Retirement plan with no expiration date. Can I still cash it? "All our X" vs. "all of our X" Is the word "of" optional in this instance? Is either of these considered preferable to the other?        Taste all our delicious treats.   Taste all of our delicious treats.