( 37035 331 ) {\displaystyle \left({\frac {37035}{331}}\right)} = ( 294 331 ) {\displaystyle =\left({\frac {294}{331}}\right)} = 1 ⋅ ( 2 331 ) ( 147 331 ) {\displaystyle =1\cdot \left({\frac {2}{331}}\right)\left({\frac {147}{331}}\right)} = − ( 147 331 ) {\displaystyle =-\left({\frac {147}{331}}\right)} = ( 331 147 ) {\displaystyle =\left({\frac {331}{147}}\right)} = ( 37 147 ) {\displaystyle =\left({\frac {37}{147}}\right)} = ( 147 37 ) {\displaystyle =\left({\frac {147}{37}}\right)} = ( 36 37 ) {\displaystyle =\left({\frac {36}{37}}\right)} = ( 2 37 ) 2 ( 9 37 ) {\displaystyle =\left({\frac {2}{37}}\right)^{2}\left({\frac {9}{37}}\right)} = ( 37 9 ) {\displaystyle =\left({\frac {37}{9}}\right)} = ( 1 9 ) = 1. {\displaystyle =\left({\frac {1}{9}}\right)=1.}

Vì 331 là số nguyên tố nên từ đó 37035 là thặng dư bậc hai mod 331.