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(p-1)/x, where p = prime(n) and x = ord(4,p), the smallest positive integer such that 4^x == 1 mod p.
+10
6
0, 2, 2, 2, 2, 2, 4, 2, 2, 2, 6, 2, 4, 6, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 4, 2, 2, 2, 6, 8, 18, 2, 4, 2, 2, 10, 6, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 6, 2, 6, 8, 2, 20, 10, 32, 2, 2, 2, 6, 8, 6, 2, 6, 2, 4, 2, 22, 16, 2, 2, 8, 2, 2, 2, 2, 2, 2, 18, 4, 4, 2, 2, 10, 12
MATHEMATICA
nn = 4; Table[If[Mod[nn, p] == 0, 0, (p-1)/MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
(p-1)/x, where p = prime(n) and x = ord(5,p), the smallest positive integer such that 5^x == 1 mod p.
+10
6
1, 1, 0, 1, 2, 3, 1, 2, 1, 2, 10, 1, 2, 1, 1, 1, 2, 2, 3, 14, 1, 2, 1, 2, 1, 4, 1, 1, 4, 1, 3, 2, 1, 2, 4, 2, 1, 3, 1, 1, 2, 12, 10, 1, 1, 6, 6, 1, 1, 2, 1, 2, 6, 10, 1, 1, 4, 10, 1, 2, 1, 1, 1, 2, 39, 1, 2, 3, 1, 2, 1, 2, 3, 1, 18, 1, 4, 1, 16, 24, 2, 2, 2, 1
MATHEMATICA
nn = 5; Table[If[Mod[nn, p] == 0, 0, (p-1)/MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
(p-1)/x, where p = prime(n) and x = ord(6,p), the smallest positive integer such that 6^x == 1 mod p.
+10
6
0, 0, 4, 3, 1, 1, 1, 2, 2, 2, 5, 9, 1, 14, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 8, 10, 1, 1, 1, 1, 1, 1, 1, 6, 4, 1, 1, 6, 2, 4, 1, 3, 10, 2, 14, 1, 2, 1, 1, 1, 1, 14, 12, 1, 1, 2, 2, 1, 1, 5, 2, 2, 6, 62, 6, 2, 2, 6, 1, 3, 11, 2, 1, 1, 6, 2, 4, 1, 1, 24, 1, 15, 10
MATHEMATICA
nn = 6; Table[If[Mod[nn, p] == 0, 0, (p-1)/MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
(p-1)/x, where p = prime(n) and x = ord(7,p), the smallest positive integer such that 7^x == 1 mod p.
+10
6
1, 2, 1, 0, 1, 1, 1, 6, 1, 4, 2, 4, 1, 7, 2, 2, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 4, 8, 1, 2, 2, 2, 2, 1, 3, 1, 2, 1, 1, 15, 19, 8, 2, 2, 1, 6, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 14, 2, 1, 2, 10, 3, 2, 3, 6, 1, 1, 11, 1, 6, 6, 1, 2, 4, 1, 2, 17, 22, 6, 1, 1, 6
MATHEMATICA
nn = 7; Table[If[Mod[nn, p] == 0, 0, (p-1)/MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
(p-1)/x, where p = prime(n) and x = ord(9,p), the smallest positive integer such that 9^x == 1 mod p.
+10
6
1, 0, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 10, 2, 2, 2, 2, 12, 6, 2, 12, 2, 2, 2, 4, 2, 6, 2, 4, 2, 2, 2, 2, 2, 2, 6, 4, 2, 2, 2, 2, 4, 2, 24, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 18, 4, 2, 2, 2, 18, 2, 8, 2, 2, 4, 2, 4, 2, 2, 6, 4, 2, 2, 2, 4, 2, 4, 2, 4, 10, 16
MATHEMATICA
nn = 9; Table[If[Mod[nn, p] == 0, 0, (p-1)/MultiplicativeOrder[nn, p]], {p, Prime[Range[100]]}]
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