The Problem: ( 270 + 370 ) is divisible by which number? [ 5, 13, 11 , 7 ]  Using Fermat's little theorem it took more than the double of the indicated time limit. But I would like to solve it quickly as I am preparing for an exam, that would require us to solve each MCQs to be solved in 4 minutes on an average.    Thanks in advance.
Show that $13$ divides $2^{70} + 3^{70}$.   My main problem here is trying to figure out how to separate the two elements in the sum, and then use Fermat's little theorem. So how can I separate the two?  Thanks!
What is a complete book for introductory quantum field theory? There's a fairly standard two or three-semester curriculum for introductory quantum field theory, which covers topics such as:   classical field theory background canonical quantization, path integrals the Dirac field quantum electrodynamics computing $S$-matrix elements in perturbation theory, decay rates, cross sections renormalization at one loop Yang-Mills theory spontaneous symmetry breaking the Standard Model   What is a good, complete and comprehensive book that covers topics such as these? Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$ Somewhere on Stack Exchange I saw the equation     $$\gcd(2^m-1,2^n-1)=2^{\gcd(m,n)}-1.$$   I had never seen this before, so I started trying to prove it. Without success...  Can anyone explain me (so actually prove) why this equation is true?  And can we say the same when replacing the '$2$' by any integer number '$a$'? I recently found a bug, which I mentioned on , as well as submitting a case, and after a few days fumbling around with the case, they closed it by saying that they only provide this type of support for Premier Support customers.  Is there a better channel for reporting bugs than by submitting a case, or is there something "special" we have to do? I realize this question is similar to , except that I've already gone the route of , as suggested by the answer there (i.e. submitting a case), to no avail.  How can I make sure that a bug like this can find its way to someone capable of at least confirming that the behavior was expected? This behavior isn't documented anywhere, and so I assume that it's a bug that needs to be addressed. Few days ago I got sample of toroidal core from my friend. I don't know any technical details of core just know OD-10cm, ID-6cm, height- 5cm and wet about 1.845 kg(M4 grade CRGO). I want to make toroidal transformer using this core but how to calculate core area and maximum VA capacity of core.I take some photos and attach. Length of a JavaScript object I have a JavaScript object. Is there a built-in or accepted best practice way to get the length of this object? const myObject = new Object(); myObject[&quot;firstname&quot;] = &quot;Gareth&quot;; myObject[&quot;lastname&quot;] = &quot;Simpson&quot;; myObject[&quot;age&quot;] = 21; Raised index of partial derivative I have eight independent variables and one dependent.  I have run a correlation matrix, and 5 of them have a low correlation with the DV.  I have then run a stepwise multiple regression to see whether any/all of the IVs can predict the DV.  The regression showed that only two IVs can predict the DV (can only account for about 20% of the variance though), and SPSS removed the rest from the model.  My supervisor reckons that I have not run the regression correctly, as due to the strength of the correlations, I should have found more predictors in the regression model. But the correlations were tiny, so my question is: if IVs and the DV hardly correlate, can IVs still be good predictors of the DV? How to get back to a site when viewing one of its questions When viewing a question on a site which I don't use (I never registered on it), I can't figure out how to get back to the list of questions of the site.  See this example  from the Stack Exchange Android app. Where should I click to see the list of questions? (I chose Mathematics Educators because it's the most recent site, it is very likely that most users don't have an account on this website)  Here is a random example:    When viewing a question, I don't know how to view the list of questions. This site can't be found in the sidebar since it's not in my Your Sites list. The top menu containing the site's title only opens the sidebar. Why do I get TypeError: can't multiply sequence by non-int of type 'float'? Why was the alien threat in The Next Generation episode "Conspiracy" never followed up? In the Star Trek The Next Generation episode  Picard and crew are drawn into an alien conspiracy to take over the Federation. This ends with Picard and Riker destroying an alien "mother" beast, but not before it manages to send a signal to an uncharted sector of space. The feeling at the end of the episode is that this will be a threat that the intrepid crew of the Enterprise would be facing again at some point, but this never happens.   Why was the implied threat at the end of this episode never brought up again on the show? Headline Language Is there a particular term for the abbreviated language used in headlines (the removal of at least articles and conjunctions)? Is there any way other than instanceof operator for object type comparison in java? I remember reading in some Java book about any operator other than 'instanceof' for comparing the type hierarchy between two objects.  instanceof is the most used and common. I am not able to recall clearly whether there is indeed another way of doing that or not. How to nest code within a list using Markdown How can I add text in a non-english language? How can I add text with non Latin characters? I'd like to get text in other languages like Arabic, Russin (Cyrilic), Japanese, Chinese, Malayalam among others, but I get rectangles instead of Arabic letters. Input password into SSH without typing changed primary email in google account. how to log in? I added gmail to my google account. Now when i try to log into stack exchange using google it prompts me to create a new account instead of using the existing.   The google account is still the same but google changed the primary email adress.  How can i log in again? How to find the build / version of Windows 10 During the beta of Windows 10 it was hard know what version you were running unless it had it posted to the desktop. Once that wasn't there - how do you tell what version / build you are running?   This will become more of an issue as Microsoft starts releasing more builds with the new update mechanism. Publicity badges might be taking internal links into account? I have a very simple jQuery Datepicker calendar:  $(document).ready(function(){     $("#date_pretty").datepicker({      }); });   and of course in the HTML...  &lt;input type="text" size="10" value="" id="date_pretty"/&gt;   Today's date is nicely highlighted for the user when they bring up the calendar, but how do I get jQuery to pre-populate the textbox itself with today's date on page load, without the user doing anything?  99% of the time, the today's date default will be what they want. How can I change the color of the lines (the frame) in a tabular environment? In the following MWE:  \begin{tabular}{c|c|c} a&amp;b&amp;c \\ \hline d&amp;e&amp;f \\ \hline g&amp;h&amp;i \end{tabular}   I would like the horizontal and vertical lines of the table to have, say a blue color.