${\displaystyle \left({\frac {1117}{1861}}\right)}$ = ${\displaystyle \left({\frac {1861}{1117}}\right)}$ = ${\displaystyle \left({\frac {744}{1117}}\right)}$ = ${\displaystyle \left({\frac {2^{3}}{1117}}\right)}$ ${\displaystyle \left({\frac {3}{1117}}\right)}$ ${\displaystyle \left({\frac {31}{1117}}\right)}$ = ${\displaystyle (-1)\left({\frac {1117}{3}}\right)\left({\frac {1117}{31}}\right)}$ = ${\displaystyle (-1)\left({\frac {1}{3}}\right)\left({\frac {1}{31}}\right)}$ = ${\displaystyle -1}$ .
Also ist ${\displaystyle 1117}$ kein Quadratrest modulo ${\displaystyle 1861}$.