Determine the quadratic residues modulo 13Solutionwe find li

Determine the quadratic residues modulo 13.

Solution

we find list of all quadratic residues

1^2 = 12^2 = 1

2^2 = 11^2 =4

3^2 = 10^2 = 9

4^2 = 9^2 = 3

5^2 =8^2 = 12

6^2 = 7^2 = 10

7^2 = 6^2 = 10

8^2 = 5^2 = 12

9^2 = 4^2 = 3

10^2 = 3^2 = 9

11^2 = 2^2 = 6

12^2 = 1^2 =1

Quadratic residues are

{1 , 3, 4 , 6 , 9 , 10 , 12} ..........Answer