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A060965
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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.
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0
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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, 102, 115, 108, 106, 114, 106, 132, 138, 115, 150, 169, 142, 187, 168, 174, 180, 187, 192, 169, 198, 187, 223, 250, 228, 250, 234, 240, 223, 252, 258, 264, 270, 241, 250
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OFFSET
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0,1
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COMMENTS
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Note that the number of points is p+1 when p+1=0 (mod 3); p is a prime in A003627.
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LINKS
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EXAMPLE
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a(2) = 4 because over GF(3) the points on the curve are (0,1), (1,0), (2,2) and the point at infinity.
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MATHEMATICA
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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)
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CROSSREFS
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Cf. A098514 (number of points on the elliptic curve y^2 = x^3 + x + 1 (mod prime(n))).
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001
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EXTENSIONS
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Edited and extended by T. D. Noe, Sep 14 2004
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STATUS
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approved
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