OFFSET
0,8
COMMENTS
a(n) is minimum e for which 11^e == +-1 (mod n), or zero if no such e exists.
For n > 2, a(n) <= (n-1)/2. - Robert Israel, Mar 20 2020
REFERENCES
H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Multiplicative Order.
S. Wolfram, Algebraic Properties of Cellular Automata (1984), Appendix B.
MAPLE
f:= proc(n) local x;
if n mod 11 = 0 then return 0 fi;
x:= numtheory:-mlog(-1, 11, n);
if x <> FAIL then x else numtheory:-order(11, 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[11, n];
CROSSREFS
KEYWORD
AUTHOR
Harry J. Smith, Feb 08 2005
STATUS
approved