问题及解答

对于 $n=1,2,\ldots,10$, 计算 $\Bigl(\frac{n}{11}\Bigr)$.

==> v:=sqvec(11).
-: (0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100)

==> w:=v mod 11.
-: (0, 1, 4, 9, 5, 3, 3, 5, 9, 4, 1)

因此

\[
n^2\equiv (0,1,4,9,5,3) \mod 11
\]

故,

\[
\Bigl(\frac{n}{11}\Bigr)=\begin{cases}
1, & n=1,4,9,5,3,\\
-1, & n=2,6,7,8,10.
\end{cases}
\]