

A086966


Number of distinct zeros of x^4x1 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
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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), 429440, see pp. 433434.


MATHEMATICA

Table[p=Prime[n]; cnt=0; Do[If[Mod[x^4x1, p]==0, cnt++ ], {x, 0, p1}]; 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



