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Search: id:A086967
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| A086967 |
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Number of distinct zeros of x^5-x-1 mod prime(n). |
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+0
4
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| 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; listen)
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OFFSET
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1,7
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COMMENT
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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 (noe(AT)sspectra.com), Aug 12 2004
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LINKS
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J.-P. Serre, On a theorem of Jordan, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see p. 435.
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A086937, A086965, A086966.
Sequence in context: A025904 A137993 A059883 this_sequence A098490 A029419 A165105
Adjacent sequences: A086964 A086965 A086966 this_sequence A086968 A086969 A086970
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 24 2003
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Sep 24 2003
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