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%I #6 Mar 30 2012 17:22:28
%S 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,
%T 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,
%U 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
%N Number of distinct zeros of x^5-x-1 mod prime(n).
%C 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
%H 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 p. 435.
%t 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)
%Y Cf. A086937, A086965, A086966.
%K nonn
%O 1,7
%A _N. J. A. Sloane_, Sep 24 2003
%E More terms from _T. D. Noe_, Sep 24 2003
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