 My Math Forum Where is the problem?? Norm residue symbol
 User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 October 24th, 2018, 12:41 PM #1 Newbie   Joined: Jul 2018 From: morocco Posts: 26 Thanks: 0 Math Focus: algebraic number theory Where is the problem?? Norm residue symbol Hello Let $p$ be a rational prime such that $p\equiv 3\mod 8$ and let $\mathfrak p$ the unique prime ideal of $\mathbb{Q}(i)$ laying over $p$. Applying the norm residue properties i get : 1) $\left(\frac{2,p}{\mathfrak p}\right)=\left(\frac{2}{\mathfrak p}\right)^{v_{\mathfrak p}(p)}= \left( \frac{2}{\mathfrak p} \right)=(-1)^{\frac{p^2-1}{8}}=-1$ 2) $\left(\frac{2,p}{\mathfrak p}\right)=\left(\frac{N_{\mathbb Q(i)/\mathbb Q} (2),p}{ p}\right)=\left(\frac{4,p}{ p}\right)=1$. !! what is the mistake?? Tags norm, problem, residue, symbol 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 unm Number Theory 4 December 1st, 2012 04:42 PM omega Complex Analysis 1 March 15th, 2012 07:19 AM onako Linear Algebra 0 February 1st, 2012 12:59 AM pascal4542 Complex Analysis 1 December 3rd, 2009 10:06 AM lobstertail Advanced Statistics 0 April 17th, 2009 11:33 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top       