This question seems like it should be easy, but it's destroying me. Discriminant is -84, minkowski bound is 5.8ish so that we only need consider p=2,3,5. Let root(-21)=r, then Kummer factorization gives that
2R=(2, 1+ r)^2,
it seems apparent we are supposed to adjoin two of the square roots of 2,3,5, or 7 (or perhaps root -2,-3,-5,-7). correct me if this is wrong. By taking Norms we see any element in our extension generating a principal ideal that divides 2R has norm 2, similarly for 3R has norm 3, and for 5R has norm 5. This is as far as I've seriously gotten: I've tooled around for a while with adjoining pairs and checking for elements of valid norms (which I list below) but nothing has worked. I am thinking I may need to focus more on adjoining negative roots.
Considering real roots, elements of norm 2 are sqrt(2), sqrt(3)-1, sqrt(7)-sqrt(5), sqrt(5)-sqrt(3), and their conjugates (I'm definitely missing some good candidates but these seem reasonable). Elements of norm 3 are sqrt(3), sqrt(5)-sqrt(2), sqrt(7)-2, etc. Elements of norm 5 are sqrt(5), sqrt(7)-sqrt(2), 2sqrt(2)-sqrt(3), etc. Essentially I think that it is not possible to have an element of norm 5 by adjoining both sqrt(3), sqrt(7) but I honestly have no clue.
If some of this makes no sense, I apologize because these computations are proving pretty difficult for me to wrap my head around. Can someone suggest a valid pair along with perhaps some generators? Thank you!
I also need to pick up new knee pads since my old ones got shattered towards the end of my playing time. I’m in chicago so i wouldn’t be surprised if the rinks are still under some limited capacity near me.
The fog was so thick you couldn't be seen, very clever and I look forward to seeing your art on my next walk
I live in rural America. How many companies can I expect to offer toll road services to my house without government getting in the way?
The alternate United States of America is something occasionally used in fiction but what would be your new states [let's assume you could add 10 more states to the U.S.]?
What do you think the state would be like culturally, geographically etc., and in terms of demographics, political voting etc.? What would the food be like?
I'm interested to know.
I want to build this bed.
How do I go about adjoining the 4x4's? Just wood glue?
Haven't bought any since my kids took up the sport a few years back.
Let's call this what it is...."Jewish Lightning". It is a derogatory but very true term that many of you living in urban areas should be familiar with.
I'm kinda freaked out now and won't be staying there tonight. Short form question is, what should be the first legal action I take tomorrow? None of my stuff is destroyed technically, but the house is filled with acrid smoke leftovers and who knows when these fuckfaces might be back. I'm just really pissed off and trying to find something constructive to direct this energy towards. Yea, I live in a place that leaves much to be desired but the price is right, however, this crossed a line.
The firemen and cops seemed to know what's up and were fairly casual about it. I'm a bit more upset, as this extremely intense fire happened about 20ft from where I sleep. Any help, or just telling me to have a beer, a toke, and chill would be appreciated. Thanks.