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A086965
Number of distinct zeros of x^3-x-1 mod prime(n).
5
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 24 2003
STATUS
approved