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A103491
Multiplicative suborder of 5 (mod n) = sord(5, n).
1
0, 0, 1, 1, 1, 0, 1, 3, 2, 3, 0, 5, 2, 2, 3, 0, 4, 8, 3, 9, 0, 3, 5, 11, 2, 0, 2, 9, 6, 7, 0, 3, 8, 10, 8, 0, 6, 18, 9, 4, 0, 10, 3, 21, 5, 0, 11, 23, 4, 21, 0, 16, 4, 26, 9, 0, 6, 18, 7, 29, 0, 15, 3, 3, 16, 0, 10, 11, 16, 11, 0, 5, 6, 36, 18, 0, 9, 30, 4, 39, 0, 27, 10, 41, 6, 0, 21, 7, 10, 22, 0
OFFSET
0,8
COMMENTS
a(n) is minimum e for which 5^e = +/-1 mod n, or zero if no e exists.
For n > 2, a(n) <= (n-1)/2, with equality if (but not only if) n is in A019335. - Robert Israel, Mar 20 2020
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.
Eric Weisstein's World of Mathematics, Suborder Function
MAPLE
f:= proc(n) local x;
if n mod 5 = 0 then return 0 fi;
x:= numtheory:-mlog(-1, 5, n);
if x <> FAIL then x else numtheory:-order(5, n) fi
end proc:
f(1):= 0:
map(f, [$0..100]); # Robert Israel, Mar 20 2020
MATHEMATICA
Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[5, n];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)
CROSSREFS
Cf. A019335.
Sequence in context: A286249 A239146 A324052 * A268932 A089306 A244996
KEYWORD
easy,nonn
AUTHOR
Harry J. Smith, Feb 08 2005
STATUS
approved