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

Author

N. J. A. Sloane, Sep 24 2003

Keywords

• nonn

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.

Crossrefs

Cf. A086937, A086966, A086967.

Programs

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 *)

Formula

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