2 = 2 ^ 1
sqrt( 1 mod 2 ) = 1
    
4 = 2 ^ 2
sqrt( 1 mod 4 ) = 1
sqrt( 1 mod 4 ) = 1

8 = 2 ^ 3
sqrt( 1 mod 8 ) = 1
sqrt( 1 mod 8 ) = 1
sqrt( 1 mod 8 ) = 1
sqrt( 1 mod 8 ) = 1

16 = 2 ^ 4
sqrt( 1 mod 16 ) = 1
sqrt( 9 mod 16 ) = 5
sqrt( 9 mod 16 ) = 5
sqrt( 1 mod 16 ) = 1
sqrt( 1 mod 16 ) = 1
sqrt( 9 mod 16 ) = 5
sqrt( 9 mod 16 ) = 5
sqrt( 1 mod 16 ) = 1

32 = 2 ^ 5
sqrt( 1 mod 32 ) = 1
sqrt( 9 mod 32 ) = 13
sqrt( 25 mod 32 ) = 5
sqrt( 17 mod 32 ) = 9
sqrt( 17 mod 32 ) = 9
sqrt( 25 mod 32 ) = 5
sqrt( 9 mod 32 ) = 13
sqrt( 1 mod 32 ) = 1
sqrt( 1 mod 32 ) = 1
sqrt( 9 mod 32 ) = 13
sqrt( 25 mod 32 ) = 5
sqrt( 17 mod 32 ) = 9
sqrt( 17 mod 32 ) = 9
sqrt( 25 mod 32 ) = 5
sqrt( 9 mod 32 ) = 13
sqrt( 1 mod 32 ) = 1

64 = 2 ^ 6
sqrt( 1 mod 64 ) = 1
sqrt( 9 mod 64 ) = 29
sqrt( 25 mod 64 ) = 5
sqrt( 49 mod 64 ) = 25
sqrt( 17 mod 64 ) = 9
sqrt( 57 mod 64 ) = 21
sqrt( 41 mod 64 ) = 13
sqrt( 33 mod 64 ) = 17
sqrt( 33 mod 64 ) = 17
sqrt( 41 mod 64 ) = 13
sqrt( 57 mod 64 ) = 21
sqrt( 17 mod 64 ) = 9
sqrt( 49 mod 64 ) = 25
sqrt( 25 mod 64 ) = 5
sqrt( 9 mod 64 ) = 29
sqrt( 1 mod 64 ) = 1
sqrt( 1 mod 64 ) = 1
sqrt( 9 mod 64 ) = 29
sqrt( 25 mod 64 ) = 5
sqrt( 49 mod 64 ) = 25
sqrt( 17 mod 64 ) = 9
sqrt( 57 mod 64 ) = 21
sqrt( 41 mod 64 ) = 13
sqrt( 33 mod 64 ) = 17
sqrt( 33 mod 64 ) = 17
sqrt( 41 mod 64 ) = 13
sqrt( 57 mod 64 ) = 21
sqrt( 17 mod 64 ) = 9
sqrt( 49 mod 64 ) = 25
sqrt( 25 mod 64 ) = 5
sqrt( 9 mod 64 ) = 29
sqrt( 1 mod 64 ) = 1

3 = 3 ^ 1
sqrt( 1 mod 3 ) = 1
sqrt( 1 mod 3 ) = 1

9 = 3 ^ 2
sqrt( 1 mod 9 ) = 1
sqrt( 4 mod 9 ) = 7
sqrt( 7 mod 9 ) = 4
sqrt( 7 mod 9 ) = 4
sqrt( 4 mod 9 ) = 7
sqrt( 1 mod 9 ) = 1

27 = 3 ^ 3
sqrt( 1 mod 27 ) = 1
sqrt( 4 mod 27 ) = 25
sqrt( 16 mod 27 ) = 4
sqrt( 25 mod 27 ) = 22
sqrt( 22 mod 27 ) = 7
sqrt( 10 mod 27 ) = 19
sqrt( 19 mod 27 ) = 10
sqrt( 13 mod 27 ) = 16
sqrt( 7 mod 27 ) = 13
sqrt( 7 mod 27 ) = 13
sqrt( 13 mod 27 ) = 16
sqrt( 19 mod 27 ) = 10
sqrt( 10 mod 27 ) = 19
sqrt( 22 mod 27 ) = 7
sqrt( 25 mod 27 ) = 22
sqrt( 16 mod 27 ) = 4
sqrt( 4 mod 27 ) = 25
sqrt( 1 mod 27 ) = 1

81 = 3 ^ 4
sqrt( 1 mod 81 ) = 1
sqrt( 4 mod 81 ) = 79
sqrt( 16 mod 81 ) = 4
sqrt( 25 mod 81 ) = 76
sqrt( 49 mod 81 ) = 7
sqrt( 64 mod 81 ) = 73
sqrt( 19 mod 81 ) = 10
sqrt( 40 mod 81 ) = 70
sqrt( 7 mod 81 ) = 13
sqrt( 34 mod 81 ) = 67
sqrt( 13 mod 81 ) = 16
sqrt( 46 mod 81 ) = 64
sqrt( 37 mod 81 ) = 19
sqrt( 76 mod 81 ) = 61
sqrt( 79 mod 81 ) = 22
sqrt( 43 mod 81 ) = 58
sqrt( 58 mod 81 ) = 25
sqrt( 28 mod 81 ) = 55
sqrt( 55 mod 81 ) = 28
sqrt( 31 mod 81 ) = 52
sqrt( 70 mod 81 ) = 31
sqrt( 52 mod 81 ) = 49
sqrt( 22 mod 81 ) = 34
sqrt( 10 mod 81 ) = 46
sqrt( 73 mod 81 ) = 37
sqrt( 67 mod 81 ) = 43
sqrt( 61 mod 81 ) = 40
sqrt( 61 mod 81 ) = 40
sqrt( 67 mod 81 ) = 43
sqrt( 73 mod 81 ) = 37
sqrt( 10 mod 81 ) = 46
sqrt( 22 mod 81 ) = 34
sqrt( 52 mod 81 ) = 49
sqrt( 70 mod 81 ) = 31
sqrt( 31 mod 81 ) = 52
sqrt( 55 mod 81 ) = 28
sqrt( 28 mod 81 ) = 55
sqrt( 58 mod 81 ) = 25
sqrt( 43 mod 81 ) = 58
sqrt( 79 mod 81 ) = 22
sqrt( 76 mod 81 ) = 61
sqrt( 37 mod 81 ) = 19
sqrt( 46 mod 81 ) = 64
sqrt( 13 mod 81 ) = 16
sqrt( 34 mod 81 ) = 67
sqrt( 7 mod 81 ) = 13
sqrt( 40 mod 81 ) = 70
sqrt( 19 mod 81 ) = 10
sqrt( 64 mod 81 ) = 73
sqrt( 49 mod 81 ) = 7
sqrt( 25 mod 81 ) = 76
sqrt( 16 mod 81 ) = 4
sqrt( 4 mod 81 ) = 79
sqrt( 1 mod 81 ) = 1

243 = 3 ^ 5
sqrt( 1 mod 243 ) = 1
sqrt( 4 mod 243 ) = 241
sqrt( 16 mod 243 ) = 4
sqrt( 25 mod 243 ) = 238
sqrt( 49 mod 243 ) = 7
sqrt( 64 mod 243 ) = 235
sqrt( 100 mod 243 ) = 10
sqrt( 121 mod 243 ) = 232
...
sqrt( 121 mod 243 ) = 232
sqrt( 100 mod 243 ) = 10
sqrt( 64 mod 243 ) = 235
sqrt( 49 mod 243 ) = 7
sqrt( 25 mod 243 ) = 238
sqrt( 16 mod 243 ) = 4
sqrt( 4 mod 243 ) = 241
sqrt( 1 mod 243 ) = 1

729 = 3 ^ 6
sqrt( 1 mod 729 ) = 1
sqrt( 4 mod 729 ) = 727
sqrt( 16 mod 729 ) = 4
sqrt( 25 mod 729 ) = 724
sqrt( 49 mod 729 ) = 7
sqrt( 64 mod 729 ) = 721
sqrt( 100 mod 729 ) = 10
sqrt( 121 mod 729 ) = 718
...
sqrt( 121 mod 729 ) = 718
sqrt( 100 mod 729 ) = 10
sqrt( 64 mod 729 ) = 721
sqrt( 49 mod 729 ) = 7
sqrt( 25 mod 729 ) = 724
sqrt( 16 mod 729 ) = 4
sqrt( 4 mod 729 ) = 727
sqrt( 1 mod 729 ) = 1

5 = 5 ^ 1
sqrt( 1 mod 5 ) = 1
sqrt( 4 mod 5 ) = 3
sqrt( 4 mod 5 ) = 3
sqrt( 1 mod 5 ) = 1

25 = 5 ^ 2
sqrt( 1 mod 25 ) = 1
sqrt( 4 mod 25 ) = 23
sqrt( 9 mod 25 ) = 3
sqrt( 16 mod 25 ) = 21
sqrt( 11 mod 25 ) = 6
sqrt( 24 mod 25 ) = 18
sqrt( 14 mod 25 ) = 8
sqrt( 6 mod 25 ) = 16
sqrt( 21 mod 25 ) = 11
sqrt( 19 mod 25 ) = 13
sqrt( 19 mod 25 ) = 13
sqrt( 21 mod 25 ) = 11
sqrt( 6 mod 25 ) = 16
sqrt( 14 mod 25 ) = 8
sqrt( 24 mod 25 ) = 18
sqrt( 11 mod 25 ) = 6
sqrt( 16 mod 25 ) = 21
sqrt( 9 mod 25 ) = 3
sqrt( 4 mod 25 ) = 23
sqrt( 1 mod 25 ) = 1