Quadractic Residues n of d Element of $B_{d,n}$ Element of $P_{d,n}$
1 (33, 8, 1)
2 ?? (??, ??, 2)
4 (66, 16, 4)
8 (5, 1, 8)
9 (99, 24, 9)
13 (9, 2, 13)
15 ?? (??, ??, 15)
16 (13, 3, 16)
Problem 3 (20 points)
For the prime number 13, determine
1. for each quadratic residue $r$ of 13 determine whether $B_{13,r}$ is nonempty. (5 points)
2. for each quadratic residue $r$ of 13 for each $\equiv_{13}$ equivalence class for which there are fundamental
solutions the fundamental solutions for that equivalence $\equiv_{13}$ class in $B_{13,r}$ (5 points)
3. for quadratic residues $r$ of 13 for which $B_{13,r}$ is nonempty, the number of $\equiv_{13}$ equivalence classes.
(10 points)
