
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
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) $\left(\frac{2,p}{\mathfrak p}\right)=\left(\frac{2}{\mathfrak p}\right)^{v_{\mathfrak p}(p)}= \left( \frac{2}{\mathfrak p} \right)=(1)^{\frac{p^21}{8}}=1$ 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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Modulo Residue problem  unm  Number Theory  4  December 1st, 2012 05:42 PM 
Mistake with a simple residue problem!  omega  Complex Analysis  1  March 15th, 2012 08:19 AM 
Matrix norm optimization problem  onako  Linear Algebra  0  February 1st, 2012 01:59 AM 
residue  pascal4542  Complex Analysis  1  December 3rd, 2009 11:06 AM 
PDF of the 2norm  lobstertail  Advanced Statistics  0  April 17th, 2009 12:33 PM 