cp's OEIS Frontend

A271229 Number of solutions of the congruence y^2 == x^3 + x^2 + x (mod p) as p runs through the primes.

%I A271229 #16 Sep 24 2016 04:32:11
%S A271229 2,2,7,7,15,15,15,15,15,23,39,31,47,47,47,55,63,63,63,79,63,71,79,95,
%T A271229 95,119,119,95,111,95,119,127,143,127,135,135,159,175,191,167,191,175,
%U A271229 191,191,215,215,191,215,239,207,223,223,223,271,255,255,279,279,303,255
%N A271229 Number of solutions of the congruence y^2  == x^3 + x^2 + x (mod p) as p runs through the primes.
%C A271229 The discriminant of the elliptic curve y^2  = x^3 + x^2 + x is -3.
%H A271229 Seiichi Manyama, <a href="/A271229/b271229.txt">Table of n, a(n) for n = 1..10000</a>
%F A271229 a(n) is the number of solutions of the congruence y^2  == x^3 + x^2 + x (mod prime(n)), n >= 1.
%F A271229 a(n) = prime(n) - A271230(n), n >= 1.
%e A271229 Here P(n) stands for prime(n).
%e A271229 n,  P(n), a(n)\ Solutions (x, y) modulo P(n)
%e A271229 1,   2,    2:  (0, 0), (1, 1)
%e A271229 2,   3:    2:  (0, 0), (1, 0)
%e A271229 3,   5,    7:  (0, 0), (2, 2), (2, 3), (3, 2), (3, 3),
%e A271229                (4, 2), (4, 3)
%e A271229 4,   7,    7:  (0, 0), (2, 0), (3, 2), (3, 5), (4, 0),
%e A271229                (5, 1), (5, 6)
%e A271229 5,  11,   15:  (0, 0), (1, 5), (1, 6), (2, 5), (2, 6),
%e A271229                (5, 1), (5, 10), (6, 4), (6, 7), (7, 5),
%e A271229                (7, 6), (8, 1), (8, 10), (9, 4), (9, 7)
%e A271229 ...
%e A271229 -------------------------------------------------------
%Y A271229 Cf. A159819. A271230. A271231.
%K A271229 nonn,easy
%O A271229 1,1
%A A271229 _Wolfdieter Lang_, Apr 18 2016