Ta có: $\left(\dfrac{713}{1009}\right)=\left(\dfrac{23}{1009}\right).\left(\dfrac{31}{1009}\right)$
$\left(\dfrac{23}{1009}\right)=\left(\dfrac{1009}{23}\right)=\left(\dfrac{20}{23}\right)=\left(\dfrac{4}{23}\right).\left(\dfrac{5}{23}\right)=\left(\dfrac{5}{23}\right)=\left(\dfrac{23}{5}\right)=\left(\dfrac{3}{5}\right)=-1$
$\left(\dfrac{31}{1009}\right)=\left(\dfrac{1009}{31}\right)=\left(\dfrac{17}{31}\right)=\left(\dfrac{31}{17}\right)=\left(\dfrac{14}{17}\right)=\left(\dfrac{2}{17}\right).\left(\dfrac{7}{17}\right)=\left(\dfrac{7}{17}\right)$
$\left(\dfrac{7}{17}\right)=\left(\dfrac{17}{7}\right)=\left(\dfrac{3}{7}\right)=-\left(\dfrac{7}{3}\right)=-\left(\dfrac{1}{3}\right)=-1$
Suy ra: $\left(\dfrac{713}{1009}\right)=1$, hay 713 là thặng dư bình phương của 1009.