Polynomial Diophantine equation under modulo This problem appered in my textbook and i cant solve it, it's in the chapter of the chinese reminder theorom so that's probably related. A solution or hint would be great.
Solutions of $x^2 \equiv 1 \pmod N$ I am stuck with this exercise:     Show that $\forall s &gt;0 \quad \exists N &gt;0$ such that $$x^2 \equiv 1\pmod N$$ has more than $s$ solutions.   I think I cannot use the theory if quadratic residues, because the modulus is not prime, so maybe I must prove it with square roots or roots of unity, but I don't know how to approach it at all.  Thanks for any help.
std::auto_ptr to std::unique_ptr Using "utilize" instead of "use"? "Reality" of length contraction in SR Zombies - Why do they need to feed on living animals/humans? What is the best way to iterate over a dictionary? Why does an electron shell further away from nucleus has higher energy level? Using electrical potential energy $V=\frac{1}{4\pi \varepsilon_0} \frac{Q_1 Q_2}{r}$ , a particle further away from nucleus has lower magnitude of energy.  Using Coulomb's law, a particle further away from nucleus experiences weaker attraction, hence less energy is needed to maintain orbit$^\star$ around that e-shell compared to a electron shell closer to nucleus, hence the one closer to nucleus supposedly should have higher energy.  $^\star$I know in reality $e^-$ does not orbit around a atom, but its position exists as a probability density or radial probability function. Is there a closed form solution for the following series? (Without Using Gamma Function): $$ S=\sum _{i=1}^{n-1} \frac{1}{(i+1)!} $$ I want to remove all empty lines from a file. Even if the line contains spaces or tabs it should also be removed. $f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$? Let $f:\mathbb R \to \mathbb R$ be a continuous function such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , then is it true that $f(x)=x , \forall x \in \mathbb R$ ? I can see that $f$ is bijective , hence strictly monotone . But I cannot progress further . Please help. Thanks in advance How to run BitTorrent Sync? I am in Ubuntu 12.04 (precise) 64bit and downloaded the btsync executable from  but running it doesn't seem to have any effect. Double-clicking the executable does nothing, and running ./btsync in the terminal also exits immediately without any output.  Has anyone successfully ran this under Ubuntu, and if so, is there any special configuration changes that need to be made to make it work? How to reset evolution settings to defaults? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? I have two given names and one surname. Is it a problem if I omit the surname from my ticket? I have two names as my given name in the passport and I typically just use this as my first and last name. However, my passport has a surname too which I almost never use. Due to this, I mistakenly provided my given name as first and last name.   As per the passport,  Surname : AAAA Given name(s) : BBBB CCCC   In the ticket, First name : BBBB Last name : CCCC  The credit card I've used to make this booking has my name as BBBB CCCC.  Will this create a problem at the travel time?  Update : the airline says that they can't update the name in the ticket. They are saying that since they have made a remark of the passport details boarding will not be a problem but I might face problems at immigration. Do they check name details in itenerary to exactly match passport at the time of immigration? Is that true in your experience?  Update : Travelled without any problem, neither at boarding gate, immigration nor after arrival at border police control. !! c operator, is a two NOT? How do you reopen a closed question? How can I combine two or more querysets in a Django view? I am trying to build the search for a Django site I am building, and in that search, I am searching in three different models. And to get pagination on the search result list, I would like to use a generic object_list view to display the results. But to do that, I have to merge three querysets into one. How can I do that? I've tried this: result_list = [] page_list = Page.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term)) article_list = Article.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term) |     Q(tags__icontains=cleaned_search_term)) post_list = Post.objects.filter(     Q(title__icontains=cleaned_search_term) |     Q(body__icontains=cleaned_search_term) |     Q(tags__icontains=cleaned_search_term))  for x in page_list:     result_list.append(x) for x in article_list:     result_list.append(x) for x in post_list:     result_list.append(x)  return object_list(     request,     queryset=result_list,     template_object_name='result',     paginate_by=10,     extra_context={         'search_term': search_term},     template_name=&quot;search/result_list.html&quot;)  But this doesn't work. I get an error when I try to use that list in the generic view. The list is missing the clone attribute. How can I merge the three lists, page_list, article_list and post_list? How do I restore the Unity 7 Ctrl-Alt-Numpad combination behaviour on Gnome 3? By default, instead of doing something useful, the Ctrl-Alt-Numpad key combination in Gnome 3 shoves a window in the specified direction across the entire workspace. These shortcuts do not show in the Gnome 3 keyboard settings panel; they're just there, and they're in the way.  How can I get this behavior back in Ubuntu 17.10? pgfplots external with large dataset (lualatex?) I have fairly large datasets with densely strucutred data that i cant downsampe much without loosing structure. I use TexMaker on Ubuntu 14.04LTS. I use   \usepackage{tikz,pgfplots,pgfplotstable} \pgfplotsset{compat=1.9} \usepgfplotslibrary{external} \tikzexternalize   and   \tikzsetnextfilename{figs/test1}   to externalize the figures. This works good compiling with pdflatex -shell-escape. But as the data becomes to large I am out of memory. I am trying to compile using LuaLaTeX -shell-escape instead of pdfLatex but get the following error message:   ! Package tikz Error: Sorry, the system call 'pdflatex -halt-on-error -interact ion=batchmode -jobname "figs/test1" "\def\tikzexternalrealjob{article}\input{ar ticle}"' did NOT result in a usable output file 'figs/test1' (expected one of . pdf:.jpg:.jpeg:.png:). Please verify that you have enabled system calls. For pd flatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed?   so pgfPlots seem to call pdfLatex without the appropriate -shell-escape flag and without me specifying it. How can i get this to compile in LuaLatex? or can i compile only the figures in LuaLatex and the rest in pdfLatex (the opposite of what is happening now)? I found  and  example but neither helped me...  Thankfull for help and i am also thankful for any general advice that can help me resolve the problem of ploting larger data sets in pgfplots.   Cheers /J I have a Alcatel onetouch model 50540 running android 5.1.1 as in the title. it is rooted and began uninstalling pre-installed bloatware on my device. I do not have a complete list of uninstalled apps because I had only kept track after the first few, but ill list the ones I do know about    Download Manager Downloads Talkback Hangouts Cricket Wi-Fi Manager Camera Email Onetouch Launcher   That is the essence of what I did. I do have an edited hosts file as a makeshift adblock.  Play store gives me an error code 0 to which I removed app data and tried again, same problem.  I have tried installing local apps which brings up an "app not installed" box.  Lastly I have tried do directly extract the app into /data/app and rebooting which didn't work. How to send text to Notepad in C#/Win32? I'm trying to use SendMessage to Notepad, so that I can insert written text without making Notepad the active window.  I have done something like this in the past using SendText, but that required giving Notepad focus.  Now, first I'm retrieving the Windows handle:  Process[] processes = Process.GetProcessesByName("notepad"); Console.WriteLine(processes[0].MainWindowHandle.ToString());   I've confirmed it's the right handle for Notepad, the same shown within Windows Task Manager.  [DllImport("User32.dll", EntryPoint = "SendMessage")] public static extern int SendMessage(int hWnd, int Msg, int wParam, int lParam);   From here, I haven't been able to get SendMessage to work in all my experimentation.  Am I going in the wrong direction? Printer not recognized on Ubuntu Libre Office I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice