A079327 Smallest nonnegative integer x such that b^(n-1) == b^x (mod n) for all b that are 0 < b < n.

0, 0, 0, 3, 0, 1, 0, 3, 2, 1, 0, 3, 0, 1, 2, 7, 0, 5, 0, 3, 2, 1, 0, 3, 4, 1, 8, 3, 0, 1, 0, 7, 2, 1, 10, 5, 0, 1, 2, 3, 0, 5, 0, 3, 8, 1, 0, 7, 6, 9, 2, 3, 0, 17, 14, 7, 2, 1, 0, 3, 0, 1, 2, 15, 4, 5, 0, 3, 2, 9, 0, 5, 0, 1, 14, 3, 16, 5, 0, 7, 26, 1, 0, 5, 4, 1, 2, 7, 0, 5, 6, 3, 2, 1, 22, 7, 0, 13, 8

Offset

1,4

Comments

a(n)=0 iff n=1 or n is prime.

Links

Gottfried Helms, Table of n, a(n) for n = 1..1024

Example

a(5) = 0, since for all 1 <= b < 5 it is true that b^0 == b^(5-1) (mod 5) (hence 5 is prime).
a(9) = 2, since for all 1 <= b < 9 it is true that b^2 == b^(9-1) (mod 9) (hence 9 is composite).

Mathematica

a[n_] := For[x=0, True, x++, If[Mod[Range[n-1]^(n-1), n]==Mod[Range[n-1]^x, n], Return[x]]]

Crossrefs

Sequence in context: A213543 A247254 A035640 * A340504 A242447 A238342

Adjacent sequences: A079324 A079325 A079326 * A079328 A079329 A079330

Keyword

easy,nonn

Author

Gottfried Helms, Feb 13 2003

Extensions

Edited by Dean Hickerson, Feb 15 2003

Status

approved