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A103493
Multiplicative suborder of 7 (mod n) = sord(7, n).
0
0, 0, 1, 1, 1, 2, 1, 0, 1, 3, 2, 5, 2, 6, 0, 4, 2, 8, 3, 3, 4, 0, 5, 11, 2, 2, 6, 9, 0, 7, 4, 15, 4, 10, 8, 0, 6, 9, 3, 12, 4, 20, 0, 3, 5, 12, 11, 23, 2, 0, 2, 16, 12, 13, 9, 20, 0, 3, 7, 29, 4, 30, 15, 0, 8, 6, 10, 33, 16, 22, 0, 35, 6, 12, 9, 4, 6, 0, 12, 39, 4, 27, 20, 41, 0, 16, 3, 7, 5, 44, 12
OFFSET
0,6
COMMENTS
a(n) is minimum e for which 7^e = +/-1 mod n, or zero if no e exists.
REFERENCES
H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
LINKS
Eric Weisstein's World of Mathematics, Multiplicative Order.
MATHEMATICA
Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[7, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)
CROSSREFS
Sequence in context: A078806 A173438 A376701 * A121480 A082601 A286509
KEYWORD
easy,nonn
AUTHOR
Harry J. Smith, Feb 08 2005
STATUS
approved