A086965 Number of distinct zeros of x^3-x-1 mod prime(n).

0, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 1, 3, 1, 1, 0, 0, 1, 1, 1, 1, 3, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 3, 3, 0, 1, 1, 0, 0, 1, 3, 3, 1, 1, 0, 0, 1, 1, 0, 1, 0, 3, 0, 1, 1, 1, 3, 0, 1, 3, 0, 1, 3, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 3, 1, 0, 3, 1, 1, 0, 0, 0

Offset

1,9

Comments

For the prime modulus 23, the polynomial can be factored as (x+13)^2 (x+20), showing that x=10 is a zero of multiplicity 2. The discriminant of the polynomial is -23. - T. D. Noe, Aug 12 2004

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

J.-P. Serre, On a theorem of Jordan, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see pp. 433-434.

Formula

If p = prime(n), a(n) = A030199(p) + 1.

Mathematica

Table[p=Prime[n]; cnt=0; Do[If[Mod[x^3-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 100}] (* T. D. Noe, Aug 12 2004 *)

Crossrefs

Cf. A086937, A086966, A086967.

Sequence in context: A101669 A243067 A366092 * A256572 A025463 A327686

Adjacent sequences: A086962 A086963 A086964 * A086966 A086967 A086968

Keyword

nonn

Author

N. J. A. Sloane, Sep 24 2003

Status

approved