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A086967 Number of distinct zeros of x^5-x-1 mod prime(n). 3
0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 3, 0, 1, 2, 2, 2, 3, 0, 0, 0, 1, 3, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 3, 2, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 3, 1, 3, 1, 3, 0, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,7
COMMENTS
For the prime modulus 19, the polynomial can be factored as (x+6)^2 (x^3+7x^2+13x+10), showing that x=13 is a zero of multiplicity 2. For the prime modulus 151, the polynomial can be factored as (x+9) (x+39)^2 (x^2+64x+61), showing that x=112 is a zero of multiplicity 2. The discriminant of the polynomial is 2869=19*151. - 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 p. 435.
MATHEMATICA
Table[p=Prime[n]; cnt=0; Do[If[Mod[x^5-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 100}] (from T. D. Noe)
CROSSREFS
Sequence in context: A282778 A342788 A059883 * A098490 A247138 A212627
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 April 17 13:58 EDT 2024. Contains 371764 sequences. (Running on oeis4.)