How to prove $(1+i)$ is a prime in $\mathbb{Q}(i)$?
Is it true that: $a+bi$ is prime in $\mathbb{Z}[i]$ if and only if $a^2+b^2$ is prime in $\mathbb{Z}$
I am looking for a story about the future of mankind, in which most people have been enslaved in a virtual reality. It ends with the revelation that the people are just lying there imagining their lives with their heads in a trough of feed.  It explains that chemists began to create compounds that could be released into the air to manipulate citizens - causing them to live, shop, think as desired by whoever was in charge. Eventually these tools got subtle enough that they could simulate reality using just these airborne compounds.  This was clearly a prescient view of what later became computer-based virtual reality fiction. What is the meaning of p values and t values in statistical tests? After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests.  It seems that students easily learn how to perform the calculations required by a given test but get hung up on interpreting the results.  Many computerized tools report test results in terms of "p values" or "t values".  How would you explain the following points to college students taking their first course in statistics:   What does a "p-value" mean in relation to the hypothesis being tested?  Are there cases when one should be looking for a high p-value or a low p-value? What is the relationship between a p-value and a t-value? Along the lines of , what reasons are there (if any) to favor \( ... \) over $ ... $? Is there a size limit on external USB hard drives? The internal SATA hard drives have a limit on a lot of motherboards of 2TB and if I want to get a 3TB HDD then I need to connect it using a PCI card (or get a new motherboard).  But I wanted to ask: If I connect a 3TB harddrive to a external USB enclosure, will it work? The  I want to buy says it supports up to 3TB HDD but I want to make sure. Obtaining a formula for prediction limits in a linear model (i.e.: prediction intervals) Let's take the following example:  set.seed(342) x1 &lt;- runif(100) x2 &lt;- runif(100) y &lt;- x1+x2 + 2*x1*x2 + rnorm(100) fit &lt;- lm(y~x1*x2)   This creates a model of y based on x1 and x2, using a OLS regression.  If we wish to predict y for a given x_vec we could simply use the formula we get from the summary(fit).  However, what if we want to predict the lower and upper predictions of y? (for a given confidence level).  How then would we build the formula? This is a  about DNS server administration.   I have one hundred or so domains. All of these domains need to be configured identically, but it seems like a huge waste of time to have to configure a new zone and/or zonefile for every one of these domains. There has to be a better way to automate this!  I think I'm on to something...if I create a zone called ., or use some other feature in my DNS software to always return a specific IP when an A record is requested, this seems to get me pretty close to my desired end result. My server is responding authoritatively to the requests and it's so much easier to manage!  This was working great until nameserver validation software started checking these domains. I figured out that I can make most of the errors go away by adding NS records, but my software won't let me put more than one SOA record in the same zone file.  How do I work around this multiple SOA record problem? I have used Windows since childhood, and when I hear the phrase "Windows filesystem" I think of directories (folders) within directories, a folder called SYSTEM, a folder called PROGRAM FILES etc. Is this what the system is? Just the layout of the folders?  And then I recently started using Linux, and my reference book says in the linux filesystem everything starts at root and branches off from there. How is that really different from Windows? I mean, it seems the linux system and the windows system are just two ways of setting up a directory tree.  Is this what file system means? Eigenvectors of real symmetric matrices are orthogonal Ideals in valuation rings How do I prove the fact that for any valuation ring $V$ the ideals are totally ordered under inclusion? I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. How Do I Choose Between a Hash Table and a Trie (Prefix Tree)? So if I have to choose between a hash table or a prefix tree what are the discriminating factors that would lead me to choose one over the other. From my own naive point of view it seems as though using a trie has some extra overhead since it isn't stored as an array but that in terms of run time (assuming the longest key is the longest english word) it can be essentially O(1) (in relation to the upper bound). Maybe the longest english word is 50 characters?  Hash tables are instant look up once you get the index. Hashing the key to get the index however seems like it could easily take near 50 steps.  Can someone provide me a more experienced perspective on this? Thanks! Visas to travel the world I understand that you have to have visas to enter some countries, but I was wondering whether you have to pay for each visa separately or you can get a visa to go everywhere. You see videos and lists on what you should pack to travel the world, but no lists on the documentation needed. How do you compare two version Strings in Java? How to add border to listview and different row colors at the same time How do I free up disk space? My Ubuntu cloud server has left only 900MB of disk space.   I'll just empty the directory /tmp and wondering if there is any other location to clean up. I co signed on a bank loan to finance the purchase of a car for my brother in Florida.  Only his name is on title, registration and insurance policy. Would I be liable and can I be sued by another person if he were in an accident? What is a good criterion or rule-of-thumb for determining when a control should be greyed-out and when should it be completely invisible? Get rid of the question ban on Meta; suspend actively harmful users manually I've got a custom loop that I'm using to display some Real Estate listings that will be available within 60 days. I'm calling it with the following function:   &lt;?php  $sixtydays = date('Y/m/d', strtotime('+60 days')); $paged = (get_query_var('paged')) ? get_query_var('paged') : 1; $query = new PostsOrderedByMetaQuery(array(   'post_type' =&gt; array('post', 'real-estate'),   'meta_key' =&gt; 'Time Available',   'meta_compare' =&gt; '&lt;=',   'meta_value' =&gt; $sixtydays,   'paged' =&gt; $paged,   'orderby_meta_key' =&gt; 'Price',   'orderby_order'    =&gt; 'ASC' )); ?&gt; &lt;?php while ($query-&gt;have_posts()) : $query-&gt;the_post(); ?&gt;   While the loop works great, I can't get it to paginate. It shows the first 10 (my default) posts but doesn't show the pagination. The only way to display all posts is to show them on one page by adding 'posts_per_page' =&gt; -1, I have similar loops on other pages that have no problem paginating. The only difference with this one is that there are two meta keys that are filtering the posts.   I'm using WP Page Navi for this and the rest of my pages. I'm closing the loop and adding the pagination using the following code:   &lt;?php endwhile; // End the loop. Whew. ?&gt; &lt;?php wp_pagenavi(); ?&gt; &lt;?php wp_reset_query(); ?&gt;   How can I go about fixing this? Intuitive Explanation of Tippe Top Effect?