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 Number Theory Number Theory Math Forum

 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 $K=\mathbb Q(\sqrt{2})$. How to show that : $p$ decomposes into $4$ primes of $K$ if and only if $\left(\frac{2}{ p}\right)_4=1$. thanks May 29th, 2019, 06:11 PM #2 Senior Member   Joined: Sep 2016 From: USA Posts: 670 Thanks: 440 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 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 $K$. Tags exercice, exercise Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post alfred_oh Advanced Statistics 1 April 30th, 2013 08:35 AM ManosG Real Analysis 3 March 26th, 2013 02:11 PM icemanfan Number Theory 2 March 15th, 2012 04:58 PM Touya Akira Abstract Algebra 8 May 10th, 2011 07:57 AM Noob1 Advanced Statistics 7 April 26th, 2010 05:55 AM

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