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A103495
Multiplicative suborder of 9 (mod n) = sord(9, n).
0
0, 0, 1, 0, 1, 1, 0, 3, 1, 0, 1, 5, 0, 3, 3, 0, 2, 4, 0, 9, 2, 0, 5, 11, 0, 5, 3, 0, 3, 7, 0, 15, 4, 0, 4, 6, 0, 9, 9, 0, 2, 2, 0, 21, 5, 0, 11, 23, 0, 21, 5, 0, 3, 13, 0, 10, 3, 0, 7, 29, 0, 5, 15, 0, 8, 6, 0, 11, 8, 0, 6, 35, 0, 3, 9, 0, 9, 15, 0, 39, 2, 0, 2, 41, 0, 8, 21, 0, 5, 22, 0, 3, 11, 0, 23
OFFSET
0,8
COMMENTS
a(n) is minimum e for which 9^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[9, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)
CROSSREFS
Sequence in context: A085391 A280880 A050143 * A261699 A285574 A354821
KEYWORD
easy,nonn
AUTHOR
Harry J. Smith, Feb 08 2005
STATUS
approved