My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum


Thanks Tree2Thanks
  • 2 Post By SDK
Reply
 
LinkBack Thread Tools Display Modes
May 29th, 2019, 01:56 PM   #1
Newbie
 
Joined: Jul 2018
From: morocco

Posts: 26
Thanks: 0

Math Focus: algebraic number theory
exercise

Hello
Let $p$ be a prime such that $p\equiv 1\pmod 8$ and $K=\mathbb Q(\sqrt[4]{2})$.
How to show that :
$p$ decomposes into $4$ primes of $K$ if and only if $\left(\frac{2}{ p}\right)_4=1$.

thanks
Chems is offline  
 
May 29th, 2019, 06:11 PM   #2
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 635
Thanks: 401

Math Focus: Dynamical systems, analytic function theory, numerics
This doesn't make sense. Your notation for $K$ seems to imply that $K$ is a field extension. However, fields do not contain primes so I'm not sure what you mean by the last line.
Thanks from topsquark and Chems
SDK is offline  
May 30th, 2019, 02:52 AM   #3
Newbie
 
Joined: Jul 2018
From: morocco

Posts: 26
Thanks: 0

Math Focus: algebraic number theory
Here $K$ is a number field, so we mean by a prime of $K$, a prime of the ring of integers of $K$.
Chems is offline  
Reply

  My Math Forum > College Math Forum > Number Theory

Tags
exercice, exercise



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Can anyone help me with this exercise? alfred_oh Advanced Statistics 1 April 30th, 2013 08:35 AM
Help with this exercise ManosG Real Analysis 3 March 26th, 2013 02:11 PM
brief exercise icemanfan Number Theory 2 March 15th, 2012 04:58 PM
Could someone help me with this exercise Touya Akira Abstract Algebra 8 May 10th, 2011 07:57 AM
Need help with exercise Noob1 Advanced Statistics 7 April 26th, 2010 05:55 AM





Copyright © 2019 My Math Forum. All rights reserved.