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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 (list; graph; refs; listen; history; text; internal format)
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: A345375 A101669 A243067 * A256572 A025463 A327686

Adjacent sequences:  A086962 A086963 A086964 * A086966 A086967 A086968

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 24 2003

STATUS

approved

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Last modified September 26 02:27 EDT 2021. Contains 347664 sequences. (Running on oeis4.)