What is the largest $n$ for which $n+5$ divides $n^5+5$ The largest $n$ for which $n+5$ divides $n^5+5$ is? $n$ being a natural number.
the largest integer $n$ for which $n+5$ divivides $n^5+5$? When we divide $n^5+5$ by $n+5$, we get a remainder $-620$, i.e., $n^5+5=K(n+5)-620$ , now how to proceed further?
TikZ Angle Label - Help it "fit" better? I have the following drawn with TikZ    using the code  \documentclass{article} \usepackage{tikz} \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture} \coordinate (O) at (0,0); \draw (O) circle (3); \coordinate[label = above left:$M$] (M) at (130:3); \coordinate[label = above:$N$] (N) at (80:3); \coordinate[label = below:$A$] (A) at (240:3); \coordinate[label =below right:$B$] (B) at (300:3); \draw (A) -- (M) -- (B); \draw (A) -- (N) -- (B); \tkzMarkAngle[draw = black, fill = white, opacity=1](A,M,B) \tkzLabelAngle[pos = 0.8](A,M,B){$x$} \tkzMarkAngle[pos = 0.2,draw = black, fill = white, opacity=1](A,N,B) \tkzLabelAngle [pos=0.8](A,N,B){$27 ^{\circ}$} \end{tikzpicture} \end{document}   Notice however, tht the 27 degrees does not fit in very nicely. How can I adapt the code to try and move the 27 a bit "lower" so that it fits in better, as well as the angle mark?  Also, how can I get two "double arrows" in the middle of lines AM and BN, to indicate that they are 'parallel'? What is the difference between therapy and treatment? Clicking leave closed shows the reopen pop-up Twist shifter cannot shift down – what might be the cause? My son's bike is stuck on 7. When we try to shift down to 1, there are no clicks. It just shoots right back to 7. This is a dial/twist/grip shifter, not a trigger shifter. I do not think it has anything to do with the derailleur, but want to confirm. I have one site with two languages: English and Spanish for example. What would be the proper convention to name image files?  From my point of view it would be stupid to duplicate image and then name it according to on which site it will be uploaded. It would be waste of resources IMO and unnecessary job to do.  What do you think about this one? I was wondering if there was a method to alter object settings at a set point in an animation in blender.  For example, I want to make the color of an object blue for the first 20 frames, but after 20 frames I want its color to change to green. Is there any known method of doing this? I could not find anything when I searched. Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. How do I calculate the instantaneous acceleration, rotational acceleration, and trajectory of this object, assuming it starts from rest? Show that $A_n=\sum\limits_{k=1}^n \sin k $ is bounded? Age from Date of Birth using JQuery I need to calculate if someone is over 18 from their date of birth using JQuery.  var curr = new Date(); curr.setFullYear(curr.getFullYear() - 18);  var dob = Date.parse($(this).text());  if((curr-dob)&lt;0) {     $(this).text("Under 18"); } else {     $(this).text(" Over 18"); }   There must be some easier functions to use to compare dates rather than using the setFullYear and getFullYear methods.  Note: My actual reason for wanting to find a new method is length of the code. I have to fit this code into a database field that is limited to 250 chars. Changing the database is not something that can happen quickly or easily. What is safe to exclude for a full system backup? Is it possible to extend an Indian business visa from India? I'm an Egyptian girl from Cairo. I'm planning a six-month trip to India in December for training purposes, but getting a six-month visa is so hard from my country.  If I can only get 3 months instead of 6 months, is it possible to extend the business visa in India? Notify us when the question has been edited after posting an answer How do I move Steam games to a new computer without re-downloading them? I have just bought a new computer and I have everything migrated over except for my Steam games.  I looked in Program Files/Steam/ and I found a folder full of the games I have downloaded, but I do not know if it is safe to just copy these folders from one computer to another (seeing as a lot of other applications will not work if you do this), or is there another recommended way?  I don't really feel like re-downloading all my games. I don't have the time nor bandwidth to download 20GB over a 1.5mbps connection.  Is it possible to contact Valve and get a disk with the games on it? Variables losing their values When is a gerund supposed to be preceded by a possessive adjective/determiner? Navigation bar overlapped by status bar I'm experiencing a bug where when the machine comes back from standby a monitor connected via displayport (MST) does not come back on, however the windows are still in the area it cover if it did come on.  The only way to recover from this short of a restart is to disable and reenable the display now I can do that via the command line just fine but when the display is disabled all the windows get rearranged onto the remaining screen.  Is there a way to persist the window positions and restore them so my script could do this sequence:-   enumerate windows, store positions display off (messing up positions) display on (making the display work again, yay!)  restore position of the windows   I can do step 2 and 3 just fine but I'm lost for step 1 and 4  I know I can force a position per app but that's not what I want as I could be doing different things and have the same apps in different positions, I also have multiple terminals open, I need the current positions storing somehow and restoring.  Any help would be appreciated! What is purpose of /etc/shadow and shadow cache files in Linux operating system? What is the purpose of the /etc/shadow file in Linux Operating system?  Also, is it same for SUSE clients? There is one shadow cache file is maintained what is purpose of that? Does this email mean that I have been granted the visa? I received the following email this morning. Does it mean that my visa has been granted?  UK Visas &amp; Immigration has now assessed your UK visa application and made a decision. Your documents and the decision will be sent back to either the UK Visa Application Centre where you applied, where we will contact you by email over the next few days to collect them, or if you are using the courier return service, will be sent directly back to the address provided. Please note that TLScontact does not know the outcome of the assessment and has played no role in the decision-making process. Kind regards, TLScontact UK VIsas &amp; Immigration How to convert strings into integers in Python?