The quadratic residues modulo 64 are: 0 1 4 9 16 17 25 33 36 41 49 57 
Put long screws at links:  0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60
The quadratic residues modulo 27 are: 0 1 4 7 9 10 13 16 19 22 25 
Put long screws at links:  1 2 4 5 7 8 10 11 13 14 16 17 19 20 22 23 25 26
The quadratic residues modulo 25 are: 0 1 4 6 9 11 14 16 19 21 24 
Put long screws at links:  1 3 8 13 18 20 23
The quadratic residues modulo 49 are: 0 1 2 4 8 9 11 15 16 18 22 23 25 29 30 32 36 37 39 43 44 46 
Put long screws at links:  2 4 6 9 11 13 16 18 20 23 25 27 30 32 34 37 39 41 44 46 48
The quadratic residues modulo 22 are: 0 1 3 4 5 9 11 12 14 15 16 20 
Put long screws at links:  5 6 7 8 9 10 16 17 18 19 20 21
The quadratic residues modulo 26 are: 0 1 3 4 9 10 12 13 14 16 17 22 23 25 
Put long screws at links:  1 2 3 4 5 7 12 14 15 16 17 18 20 25
The quadratic residues modulo 17 are: 0 1 2 4 8 9 13 15 16 
Put long screws at links:  2 4 5 8 9 10 13 14 16
The quadratic residues modulo 19 are: 0 1 4 5 6 7 9 11 16 17 
Put long screws at links:  2 7 8 9 10 11 12 13 18
The quadratic residues modulo 23 are: 0 1 2 3 4 6 8 9 12 13 16 18 
Put long screws at links:  0 1 2 5 7 10 11 12 14 15 20 21
The quadratic residues modulo 29 are: 0 1 4 5 6 7 9 13 16 20 22 23 24 25 28 
Put long screws at links:  0 1 3 5 6 10 13 14 15 16 19 20 21 22 25
The quadratic residues modulo 31 are: 0 1 2 4 5 7 8 9 10 14 16 18 19 20 25 28 
Put long screws at links:  1 2 3 8 9 10 13 15 18 19 21 23 24 27 29
The quadratic residues modulo 37 are: 0 1 3 4 7 9 10 11 12 16 21 25 26 27 28 30 33 34 36 
Put long screws at links:  0 3 6 8 9 10 12 15 18 19 20 22 23 24 31 32 33 35 36
The quadratic residues modulo 41 are: 0 1 2 4 5 8 9 10 16 18 20 21 23 25 31 32 33 36 37 39 40 
Put long screws at links:  0 1 4 8 11 12 15 17 22 23 24 25 26 27 28 29 30 31 36 38
The quadratic residues modulo 43 are: 0 1 4 6 9 10 11 13 14 15 16 17 21 23 24 25 31 35 36 38 40 41 
Put long screws at links:  1 2 3 4 8 9 11 13 14 15 16 17 23 25 31 32 33 34 35 37 39 40