deletions | additions       diff --git a/section_Bytes_The_polynomials_in__.tex b/section_Bytes_The_polynomials_in__.tex  index 2a6d388..01c8d5b 100644  --- a/section_Bytes_The_polynomials_in__.tex  +++ b/section_Bytes_The_polynomials_in__.tex 
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Let us consider the polynomial $g=x^2+x+1 \in \Fb[x]$ and define the set $  A \,=\, \{ \textrm{remainders by } g \} \,.  $  For this particular $g$, we have $A =\{0,1,x,x+1\}$.   We want to show that $A$ is a field. We recall the definition of field.\\  A set $A$, endowed with two operations (sum and multiplication), denoted by $+,\cdot$, field, namely that $A$  iscalled \emph{field} if  \begin{itemize}  \item[i)]$A$ is  an abelian group w.r.t.$+$; let $0$ be  the neutral element; sum of polynomials;  \item[ii)] $A\setminus\{0\}$ is an abelian group w.r.t. $\cdot$; the product of polynomials;  \item[iii)] $\cdot$ is distributive w.r.t. $+$. $(f+g)\cdot h=fh+gh$, for any $f,g,h \in A$.  \end{itemize}