My Math Forum Where is the problem?? Norm residue symbol

 Number Theory Number Theory Math Forum

 October 24th, 2018, 01:41 PM #1 Newbie   Joined: Jul 2018 From: morocco Posts: 19 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 Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post unm Number Theory 4 December 1st, 2012 05:42 PM omega Complex Analysis 1 March 15th, 2012 08:19 AM onako Linear Algebra 0 February 1st, 2012 01:59 AM pascal4542 Complex Analysis 1 December 3rd, 2009 11:06 AM lobstertail Advanced Statistics 0 April 17th, 2009 12:33 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top