Answer to Question #280677 in Combinatorics | Number Theory for John

Question

Determine whether -104 is a quadratic residue or non residue of the prime 997.

Answer 1

Solution:

(−104|997) = (−1 × 2 × 13|997)

= (−1|997)(2|997)(13|997)

= −(13|997)

= (997|13)

= −(9|13)

= −1

Therefore −104 is a quadratic nonresidue of 997.