|
| |
|
|
A060457
|
|
The number of solutions to y^2 + y = x^3 - x^2 modulo n.
|
|
2
| |
|
|
1, 4, 4, 8, 4, 16, 9, 16, 12, 16, 10, 32, 9, 36, 16, 32, 19, 48, 19, 32, 36, 40, 24, 64, 20, 36, 36, 72, 29, 64, 24, 64, 40, 76, 36, 96, 34, 76, 36, 64, 49, 144, 49, 80, 48, 96, 39, 128, 63, 80, 76, 72, 59, 144, 40, 144, 76, 116, 54, 128, 49, 96, 108, 128, 36, 160, 74
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Singh mistakenly called this the L-series, but the L-series for elliptic curve y^2 + y = x^3 - x^2 is A006571. - Michael Somos Mar 20 2010
|
|
|
REFERENCES
| Simon Singh, Fermat's last theorem, 1997 (at the end of ch. 4).
|
|
|
EXAMPLE
| a(5)=4 from the 4 solutions (0,0), (0,4), (1,0), (1,4) mod 5.
G.f.: x + 4*x^2 + 4*x^3 + 8*x^4 + 4*x^5 + 16*x^6 + 9*x^7 + 16*x^8 + 12*x^9 + ...
|
|
|
PROG
| (PARI) {a(n) = sum(x=0, n-1, sum(y=0, n-1, (y^2 + y - x^3 + x^2) % n == 0))} /* Michael Somos Mar 20 2010 */
(PARI) {a(n) = local(E, A, p, e); if(n<1, 0, E = ellinit( [0, -1, 1, 0, 0], 1); A = factor(n); prod( k=1, matsize(A)[1], if(p = A[k, 1], e = A[k, 2]; (p - ellap(E, p)) * p^(e-1) )))} /* Michael Somos Mar 20 2010 */
|
|
|
CROSSREFS
| Cf. A061011, A061012.
Sequence in context: A167275 A082075 A095727 * A163369 A028266 A165662
Adjacent sequences: A060454 A060455 A060456 * A060458 A060459 A060460
|
|
|
KEYWORD
| nonn,mult
|
|
|
AUTHOR
| Frank Ellermann (Frank.Ellermann(AT)t-online.de), Apr 09 2001
|
|
|
EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2001
|
| |
|
|
