cp's OEIS Frontend

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

%I A060457 #11 Jan 05 2024 00:12:48
%S A060457 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,
%T A060457 36,36,72,29,64,24,64,40,76,36,96,34,76,36,64,49,144,49,80,48,96,39,
%U A060457 128,63,80,76,72,59,144,40,144,76,116,54,128,49,96,108,128,36,160,74
%N A060457 Number of solutions to y^2 + y = x^3 - x^2 modulo n.
%C A060457 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
%D A060457 Simon Singh, Fermat's last theorem, 1997 (at the end of ch. 4).
%H A060457 Robin Visser, <a href="/A060457/b060457.txt">Table of n, a(n) for n = 1..10000</a>
%e A060457 a(5)=4 from the 4 solutions (0,0), (0,4), (1,0), (1,4) mod 5.
%e A060457 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 + ...
%o A060457 (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 */
%o A060457 (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 */
%Y A060457 Cf. A061011, A061012.
%K A060457 nonn,mult
%O A060457 1,2
%A A060457 _Frank Ellermann_, Apr 09 2001
%E A060457 More terms from Larry Reeves (larryr(AT)acm.org), Apr 13 2001