Exercise 3.2.5 (Some values of $\genfrac{(}{)}{}{}{p}{q}$)

Question

ewcommand{\legendre}[2]{\genfrac{(}{)}{}{}{#1}{#2}}
Find the values of $\legendre{p}{q}$ in the nine cases obtained from all combinations of $p = 7, 11, 13$, and $q = 227, 229, 1009$.

Richard Ganaye · Accepted Answer

ewcommand{\legendre}[2]{\genfrac{(}{)}{}{}{#1}{#2}}

\begin{proof} 
Values of $\legendre{p}{q}$ for $q \in \{227,229,1009\},\ p \in \{7, 11, 13\}$.
\begin{center}

\begin{tabular}{|c|ccc|}
\hline
$\ q \ \diagdown\  p$&  7 &  11 & 13 \
\hline
227 &    1& 1  & -1    \
229 &   -1 &  1 & -1  \
1009 &    1&  -1  & -1   \
\hline
\end{tabular}

\end{center}
\end{proof}
\begin{verbatim}
sage: for q in [227, 229, 1009]:
....:     print(q, [kronecker(p,q) for p in [7, 11, 13]])
....:     
(227, [1, 1, -1])
(229, [-1, 1, -1])
(1009, [1, -1, -1])
\end{verbatim}

Exercise 3.2.5 (Some values of $\genfrac{(}{)}{}{}{p}{q}$)

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Exercise 3.2.5 (Some values of $\genfrac{(}{)}{}{}{p}{q}$)

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