What is the best approach to write a literature review paper?
How to write a survey paper?
As the title, I was asked to show that $2^{44}-1$ is divisible by $89$.  My first attempt is to change the expression into $(2^{22}-1)(2^{22}+1)$.  Then further simplified it into $(2^{11}-1)(2^{11}+1)(2^{22}+1)$, I used my calculator and was able to show that $2^{11}-1$ is divisible by $89$ but then I don't know how to show it with modular arithmetic. I do think that it is quite similar to the form where we can use the Fermat's little theorem. $(\sqrt{2})^{88}-1$. (Though I do understand Flt can only be applied to integer.)  Can someone tell me whether I can take square root in modular arithmetic as well? I am still pretty new to the modular arithmetic. Thank you very much. Can I pickle a python dictionary into a sqlite3 text field? Any gotchas I should be aware of?  Can I store it in a text field, or do I need to use a blob? (I'm not overly familiar with either pickle or sqlite, so I wanted to make sure I'm barking up the right tree with some of my high-level design ideas.) Approaches to Sand on a Conveyor Belt Why does the One Ring make the wearer's clothes invisible? The One Ring turns invisible the person wearing it.  Is there an explanation for how it does this? It seems that direct contact with the skin activates the Ring's invisibility effects;  why would it also affect the person's clothing, weapons, etc, as well? The Invisible Man's clothing is visible, so why aren't Frodo's clothes visible?  The Hobbit makes it clear that Bilbo's clothing is invisible, since Smaug doesn't see it.  Is there any possiblity that this varies from character to character? If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ?  If possible, I am looking for an intuitive explanation, not a highly technical one. Get complete stats of process started/terminated during login of user account When I login, I notice many process quickly start and terminate in task manager. But it happens very fast and I cannot save details about them (like process name, command line, CPU usage,..)  How can I collect stats about them so I can view them later Local html file AJAX Call and jQuery Woes How do I use the 'scientific' mode in the Calculator? Most of us have seen on the profile page a loss of reputation citing as a reason "User was removed". This reason comes with the useful link:  which explains (emphasis mine):     This message means that a user who voted for one of your posts had their account deleted (either by request or due to violating the network's terms of service). As a result, all of their votes were removed, and the reputation you gained or lost from them was undone. The resultant reputation change could be any amount; it could even be a reputation gain if enough of the removed votes were downvotes. All the reputation changes from a single user's deletion are rolled into a single event in the reputation page labelled "User was removed".      This removal occurs whenever a user is deleted, unless that user had a very high reputation score. Because high-reputation users have usually cast a great many votes, removing all of them could be that much more disruptive to other users. In such cases, the staff use a special deletion that preserves the votes, resulting in no reputation change for those who had been voted on by that user.   However, I have got recently such a message on one of beta sites, where I have no posts. Here is  on that site. As you can see, I have only got points from association bonus,  and the last event in my reputation history is the reputation loss with the message 'User was removed'. (Notice that the post, where I made suggested edit, was not deleted. And the users who approved the posts are Community♦ and one another user, who did not delete their account.)  You can also see from  on that particular site that I have posted no questions/answers there so far. Which means there are no votes on my posts which could have been removed.     Why this did happen? How can I lose reputation points in this way if I have never made a post on that site?   I am not sure if this is a . (Feel free to remove the tag if it does not fit the question.) (EDIT: The answer and the comments posted so far indicate, that it is not a bug, so I have removed the tag from the question.) But if there is some reason why reputation posts can be lost even without having some posts and actual votes on the posts, then the description of "User was removed" seems to be a bit imprecise. (Of course, if it is a very rare edge case, it is probably not that important to have it included in the explanation.)    Just a short disclaimer: I do not care that much for the 2 points I lost. (Obviously, it would be very silly to make a fuss just for 2 points, and even more on a site which I do not frequent that much.) But if this could be indication of some hidden bug, it might be interesting to know more about this.    I have also noticed two related questions       In both cases in some answers or in comments as a possible explanation was given that probably a post, where a suggested edit was made, has been deleted. As you can see from the links I, this is not the case here. Is there any way to kill a Thread? Is it possible to terminate a running thread without setting/checking any flags/semaphores/etc.? What is the most efficient way to convert a MySQL query to CSV in PHP please?  It would be best to avoid temp files as this reduces portability (dir paths and setting file-system permissions required).  The CSV should also include one top line of field names. Can present progressive statements be use at present or for the future? or both? how to set Image and text at the center of the button Send urgent mail in Gmail Is it possible to set the "urgent" flag in Gmail for outgoing mail? I'd like to be able to flag time-sensitive emails as such. Mask and inherit the same systemd unit Suppose a package provides whatever.service file so certain events (including whatever.socket) cause a daemon to start with a certain configuration.  I want to disable this completely. In particular, I want the old socket and any other unit files that might refer to this service by name to be unable to start the daemon.  Instead, I want to create my own unit files for this daemon with a different .socket unit and different environment variables. I also want my override to automatically take account of possible upstream updates to the original unit file (which my current solution of copying whatever.service as whatever-modified.service and editing it unfortunately does not provide).  If I create the following symlinks and files: /etc/systemd/system/whatever.service → /dev/null /etc/systemd/system/whatever-modified.service → /usr/lib/systemd/system/whatever.service /etc/systemd/system/whatever-modified.service.d/fix.conf  systemd considers the new service to be masked as well and refuses to start it. How to avoid this? Emulate "double" using 2 "float"s Adjectives or compound noun? Inner automorphisms form a normal subgroup of $\operatorname{Aut}(G)$ For an arbitrary group $(G,\cdot)$ let $\operatorname{Aut}(G) = \{f: G \to G \mid f \text{ is an isomorphism}\}$ be the set of all automorphisms of the group $G$. We assume that $(\operatorname{Aut}(G),\circ)$ where $\circ$ is composition of mappings is a group.  1) Prove that for arbitrary $a \in G$ there is an automorphism $p_a: G \to G;\quad p_a(x) = a^{-1}xa$.  2) Prove, that $\operatorname{Inn}(G) = \{p_a \mid a \in G\}$ is a normal subgroup of $(\operatorname{Aut}(G),\circ)$. Grep in couple thousands files I have directory with cca 26 000 files and I need to grep in all these files. Problem is, that I need it as fast as possible, so it's not ideal to make script where grep will take name of one file from find command and write matches to file. Before "arguments list too long" issue it took cca 2 minutes to grep in all this files. Any ideas how to do it? edit: there is a script that is making new files all the time, so it's not possible to put all files to different dirs. Windows using too much RAM, how to diagnose resource hog I have 16GB of system RAM. On startup with no applications open except the task-manager Windows is using about 3gb of RAM. I looked in the processes tab, but nothing seems to be out of the ordinary. How can I find out why my Windows is using so much RAM.    all processes from all users      Reading from the poolmon it seems that my wireless broadcom driver is using about 0.4GB of of RAM. Even if I remove  it would still be using  2.6GB on start-up, which is still too much.      After reinstalling the wireless driver associated with the memory leak. I have a new screenshot and would like to confirm that it was indeed a memory leak.