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A086966 Number of distinct zeros of x^4-x-1 mod prime(n). 3
0, 0, 0, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 4, 1, 1, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 1, 2, 2, 1, 1, 1, 1, 1, 0, 0, 3, 1, 1, 0, 0, 1, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 2, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

For the prime modulus 283, the polynomial can be factored as (x+18) (x+168) (x+190)^2, showing that x=93 is a zero of multiplicity 2. The discriminant of the polynomial is 283. - T. D. Noe, Aug 12 2004

LINKS

Table of n, a(n) for n=1..100.

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

MATHEMATICA

Table[p=Prime[n]; cnt=0; Do[If[Mod[x^4-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 105}] (* T. D. Noe, Sep 24 2003 *)

CROSSREFS

Cf. A086937, A086965, A086967.

Sequence in context: A025886 A117355 A319571 * A140080 A065359 A087372

Adjacent sequences:  A086963 A086964 A086965 * A086967 A086968 A086969

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 24 2003

EXTENSIONS

More terms from T. D. Noe, Sep 24 2003

STATUS

approved

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Last modified December 12 01:57 EST 2019. Contains 329948 sequences. (Running on oeis4.)