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Accessing the index in 'for' loops? How do I access the index in a for loop like the following?  ints = [8, 23, 45, 12, 78] for i in ints:     print('item #{} = {}'.format(???, i))   I want to get this output:  item #1 = 8 item #2 = 23 item #3 = 45 item #4 = 12 item #5 = 78   When I loop through it using a for loop, how do I access the loop index, from 1 to 5 in this case? Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$ Let $p$ be prime and $(\frac{-3}p)=1$, where $(\frac{-3}p)$ is Legendre symbol. Prove that $p$ is of the form $p=a^2+3b^2$.   My progress:  $(\frac{-3}p)=1 \Rightarrow$ $(\frac{-3}p)=(\frac{-1}p)(\frac{3}p)=(-1)^{\frac{p-1}2}(-1)^{\lfloor\frac{p+1}6\rfloor}=1 \Rightarrow$ $\frac{p-1}2+\lfloor\frac{p+1}6\rfloor=2k$  I'm stuck here. This is probably not the way to prove that.  Also tried this way:  $(\frac{-3}p)=1$, thus $-3\equiv x^2\pmod{p} \Rightarrow$ $p|x^2+3 \Rightarrow$ $x^2+3=p\cdot k$ stuck here too.  Any help would be appreciated. It's time for drag and drop! I often find myself wishing SO supported drag and drop. For example I drag a tag to my favs and it would add it, or when searching by tag I would like to drag the tag to the search box and get [asp.net] added in the search box.   Does it make sense to add this feature or is it just too much work for so little use? How do I make a 3 dimensional character out of flat picture? I have a cartoon character (a lion) that is part of my business logo that I want to put into Blender and animate it somehow. Is there any way I can take a flat picture (JPEG) and transform it into a 3D image and then animate it in Blender? How to implement dual-classing in a non-levelled RPG game? I'm working on an alternate ruleset for a tabletop pen-and-paper RPG (like D&amp;D). Recently I've been toying the idea of abolishing a level system. However, I don't want to remove the ability for a player to multi-class. Are there any games which don't have a levelling system, yet allow multi-classing? How do they do it successfully? How to code around known MMa special-case failures? New tab in chromium is empty Is $\sum_{n=1}^\infty \frac{\sin(2n)}{1+\cos^4(n)}$ convergent? As I was just checking this 'child prodigy' out on Youtube, I stumbled upon  video, in which Glenn Beck asks the kid to do the following proof:    Further on, the kid starts sketching a proof (without a shadow of a doubt regarding the accuracy of his solution ) including the Integral Test. I don't know much about improper integrals since I just finished highschool, but this integral approach seemed, intuitively, pretty inaccurate to me since this is not a strictly decreasing function. Then I found this out from Wikipedia !   Furthermore, the blunt assessment that the series are convergent seems dubious as well..Upon a few computations of my own(mostly partial sums) , I tend to believe that the series are, in fact, divergent .  Can anyone suggest a rigurous take on this problem (easy as it may seem to some amongst you) ? I have setup a project of 250 frames with a flag and a wind force field. It works fine until I change the length of the project to 520 frames, then the flag is frozen after frame 250. There must be a simple way to change this. Thanks for any help. Regards, Daniel. What’s the best way to reload / refresh an iframe? I would like to reload an &lt;iframe&gt; using JavaScript. The best way I found until now was set the iframe’s src attribute to itself, but this isn’t very clean. Any ideas? Should I sign, watermark or otherwise label a framed print? And if so how? I have an opportunity to show some of my work in a small local coffee shop.  Are there any guidelines/practices to signing, labeling or watermarking a photo which is to be on display?  Or should a photo be signed, labelled or marked at all? Is signing the back of the photo and showing my name on a separate card below the frame itself the "better" way to do this?   I noticed many people on the web put a very noticeable watermark with their logo, copyright and name right on the photo.  Personally, I find this distracting as it often ruins the photograph itself often turning what could be art to kitsch. Painters most often sign the painting itself but this to me is not distracting because it is done with the painter's own hand and it often "works" with the painting. For gravity, we have    General Relativity, which is a geometric theory for gravitation.  Is there a similar analog for Electromagnetism? Chromium on Ubuntu 12.04. Youtube says:     This video is currently unavailable   I don't know why but this is the case for some videos, but not all. Well, most videos. And I don't know what's wrong.  Anyone help? What item bonuses apply to my follower? There are a lot of different side effects an item can have, and I assume that things like magic find have no influence on any of "our" found items at all.  However, I'm not sure about other things. For example:   Do followers get life-steal on weapons, too? Does increased orb healing make any difference? What about +experience after kills? Will my follower level up faster?   and probably a lot more.  Is there some general rule as to what effects of an item apply to followers, and which don't? I have seen only the first three movies, so I don't know whether the other movies/TV series deal with this question or not. My main point is that in the movies, the terminator that travels back furthest in time is of the worst quality, and the quality increases with the time travel (meaning they travelled from a later time). What is a good explanation for this?  Note: I am not interested in the obvious not-in-universe explanation that they wanted something better and bigger for each new movie. Can a concentration spell be cast without actually concentrating on it for an "instant" effect? If I am shooting the 8-ball for a win, and my opponent has a ball near the pocket I'm aiming for, can I call something like "8-ball off the 2 ball into the corner pocket"?  I thought this was allowed, but a friend says this is an automatic loss and that the 8-ball must never touch another ball before going into the pocket.  Various pool rules aren't clear for me on this scenario. Every time Windows 10 runs updates (which I see no way to control), it updates my graphics driver.  I like the old one because it is faster.  So, I have to reinstall it.  This is getting to be a pain.  Is there any way to stop Windows 10 from updating it again? Z-axis issue with the floating review info panel, permits various elements to flow over it How to justify the definition of summation $s_n=\sum_{i=1}^n a_i=a_1+\cdots+a_n$? I read  and found that they define summation via recursion, so I decided to formalize the proof that that this definition is actually valid. I've two questions:   Does my proof contain any error? Are there other simple ways to define summation?   Thank you so much!     Suppose that $(a_1,\cdots,a_n)$ is a finite sequence in $\mathbb N$. Show that there is a sequence $(s_1,\cdots,s_n)$ such that $s_1=a_1$ and $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$.   My attempt:  We define mapping $f$ as follows: $f: \mathbb N\times\mathbb N\to\mathbb N\times\mathbb N: (i,a)\mapsto\begin{cases} (i+1,a+a_{i+1})&amp;\text{if }i&lt;n\\ (i+1,a)&amp;\text{if }i\geq n \end{cases}$  By recursion theorem, there is a unique sequence $(p_i\mid i\in\mathbb N)$ such that $p_0=(1,a_1)$ and $p_{i+1}=f(p_i)$. Let $\pi:\mathbb N\times\mathbb N\to\mathbb N$ be the projection to the second co-ordinate i.e. $\pi(i,a)=a$. Let $s_i=\pi(p_i)$ for all $1\leq i\leq n$, then $(s_i\mid 1\leq i\leq n)$ is the required sequence. It's clear from the definition of $s_i$ that $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$.