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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 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.)