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A271229 Number of solutions of the congruence y^2 == x^3 + x^2 + x (mod p) as p runs through the primes. 5
2, 2, 7, 7, 15, 15, 15, 15, 15, 23, 39, 31, 47, 47, 47, 55, 63, 63, 63, 79, 63, 71, 79, 95, 95, 119, 119, 95, 111, 95, 119, 127, 143, 127, 135, 135, 159, 175, 191, 167, 191, 175, 191, 191, 215, 215, 191, 215, 239, 207, 223, 223, 223, 271, 255, 255, 279, 279, 303, 255 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The discriminant of the elliptic curve y^2 = x^3 + x^2 + x is -3.
LINKS
FORMULA
a(n) is the number of solutions of the congruence y^2 == x^3 + x^2 + x (mod prime(n)), n >= 1.
a(n) = prime(n) - A271230(n), n >= 1.
EXAMPLE
Here P(n) stands for prime(n).
n, P(n), a(n)\ Solutions (x, y) modulo P(n)
1, 2, 2: (0, 0), (1, 1)
2, 3: 2: (0, 0), (1, 0)
3, 5, 7: (0, 0), (2, 2), (2, 3), (3, 2), (3, 3),
(4, 2), (4, 3)
4, 7, 7: (0, 0), (2, 0), (3, 2), (3, 5), (4, 0),
(5, 1), (5, 6)
5, 11, 15: (0, 0), (1, 5), (1, 6), (2, 5), (2, 6),
(5, 1), (5, 10), (6, 4), (6, 7), (7, 5),
(7, 6), (8, 1), (8, 10), (9, 4), (9, 7)
...
-------------------------------------------------------
CROSSREFS
Sequence in context: A306238 A318086 A244049 * A199886 A117779 A300952
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 18 2016
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)