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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Note that the number of points is p+1 when p+1=0 (mod 3); p is a prime in A003627.

LINKS

Table of n, a(n) for n=0..58.

EXAMPLE

a(2) = 4 because over GF(3) the points on the curve are (0,1), (1,0), (2,2) and the point at infinity.

MATHEMATICA

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)

CROSSREFS

Cf. A098514 (number of points on the elliptic curve y^2 = x^3 + x + 1 (mod prime(n))).

Sequence in context: A073906 A108797 A089161 * A153883 A033162 A105133

Adjacent sequences:  A060962 A060963 A060964 * A060966 A060967 A060968

KEYWORD

nonn

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), May 09 2001

EXTENSIONS

Edited and extended by T. D. Noe, Sep 14 2004

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)