cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086965 Number of distinct zeros of x^3-x-1 mod prime(n).

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%I A086965 #16 Jan 14 2017 11:56:30
%S A086965 0,0,1,1,1,0,1,1,2,0,0,1,0,1,0,1,3,1,1,0,0,1,1,1,1,3,1,1,1,1,0,0,1,0,
%T A086965 1,0,1,0,3,3,0,1,1,0,0,1,3,3,1,1,0,0,1,1,0,1,0,3,0,1,1,1,3,0,1,3,0,1,
%U A086965 3,0,0,1,1,1,1,1,1,0,1,0,1,1,1,1,0,0,3,1,0,3,1,1,0,0,0
%N A086965 Number of distinct zeros of x^3-x-1 mod prime(n).
%C A086965 For the prime modulus 23, the polynomial can be factored as (x+13)^2 (x+20), showing that x=10 is a zero of multiplicity 2. The discriminant of the polynomial is -23. - _T. D. Noe_, Aug 12 2004
%H A086965 G. C. Greubel, <a href="/A086965/b086965.txt">Table of n, a(n) for n = 1..1000</a>
%H A086965 J.-P. Serre, <a href="http://www.ams.org/bull/2003-40-04/S0273-0979-03-00992-3/S0273-0979-03-00992-3.pdf">On a theorem of Jordan</a>, Bull. Amer. Math. Soc., 40 (No. 4, 2003), 429-440, see pp. 433-434.
%F A086965 If p = prime(n), a(n) = A030199(p) + 1.
%t A086965 Table[p=Prime[n]; cnt=0; Do[If[Mod[x^3-x-1, p]==0, cnt++ ], {x, 0, p-1}]; cnt, {n, 100}] (* _T. D. Noe_, Aug 12 2004 *)
%Y A086965 Cf. A086937, A086966, A086967.
%K A086965 nonn
%O A086965 1,9
%A A086965 _N. J. A. Sloane_, Sep 24 2003