A060457 Number of solutions to y^2 + y = x^3 - x^2 modulo n.

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

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).

Links

Robin Visser, Table of n, a(n) for n = 1..10000

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: A255485 A322328 A095727 * A339756 A163369 A290841

Adjacent sequences: A060454 A060455 A060456 * A060458 A060459 A060460

Keyword

nonn,mult

Author

Frank Ellermann, Apr 09 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2001

Status

approved