Search: id:A060965
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%I A060965
%S A060965 3,4,6,7,12,7,18,25,24,30,34,25,42,34,48,54,60,61,61,72,79,61,84,90,115,
%T A060965 102,115,108,106,114,106,132,138,115,150,169,142,187,168,174,180,187,
%U A060965 192,169,198,187,223,250,228,250,234,240,223,252,258,264,270,241,250
%N A060965 For p=prime(n), a(n) = number of points (x,y) on the elliptic curve x^3 
               + y^3 = 1 (mod p), including the point at infinity.
%C A060965 Note that the number of points is p+1 when p+1=0 (mod 3); p is a prime 
               in A003627.
%e A060965 a(2) = 4 because over GF(3) the points on the curve are (0,1), (1,0), 
               (2,2) and the point at infinity.
%t A060965 Table[p=Prime[n]; s2=Mod[Table[y^3, {y, 0, p-1}], p]; s3=Mod[Table[1-x^3, 
               {x, 0, p-1}], p]; s=Intersection[Union[s2], Union[s3]]; 1+Sum[Count[s2, 
               s[[i]]]*Count[s3, s[[i]]], {i, Length[s]}], {n, 100}] (T. D. Noe)
%Y A060965 Cf. A098514 (number of points on the elliptic curve y^2 = x^3 + x + 1 
               (mod prime(n))).
%Y A060965 Sequence in context: A073906 A108797 A089161 this_sequence A153883 A033162 
               A105133
%Y A060965 Adjacent sequences: A060962 A060963 A060964 this_sequence A060966 A060967 
               A060968
%K A060965 nonn
%O A060965 0,1
%A A060965 Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001
%E A060965 Edited and extended by T. D. Noe (noe(AT)sspectra.com), Sep 14 2004

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