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A103491
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Multiplicative suborder of 5 (mod n) = sord(5, n).
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1
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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
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OFFSET
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0,8
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COMMENTS
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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
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REFERENCES
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H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
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LINKS
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MAPLE
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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:
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MATHEMATICA
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Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[5, n];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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