Re: Integer Points on elliptic curve
- To: mathgroup at smc.vnet.net
- Subject: [mg82430] Re: [mg82411] Integer Points on elliptic curve
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 20 Oct 2007 05:48:41 -0400 (EDT)
- Reply-to: hanlonr at cox.net
Brute force method: eqn = a^2 + 1689 b^2 == c^3; soln = Select[ Flatten[Table[{a, b, (eqn[[1]])^(1/3)}, {a, 0, 2000}, {b, 0, 80}], 1], IntegerQ[Last[#]] &] {{0, 0, 0}, {1, 0, 1}, {8, 0, 4}, {27, 0, 9}, {64, 0, 16}, {125, 0, 25}, {144, 3, 33}, {205, 32, 121}, {216, 0, 36}, {241, 10, 61}, {343, 0, 49}, {434, 2, 58}, {512, 0, 64}, {729, 0, 81}, {1000, 0, 100}, {1152, 24, 132}, {1276, 29, 145}, {1331, 0, 121}, {1366, 14, 130}, {1654, 59, 205}, {1728, 0, 144}, {1928, 80, 244}} Bob Hanlon ---- Artur <grafix at csl.pl> wrote: > Who know how find by Mathematica integer solutions of elliptic equation: > a^2+1689b^2=c^3 > one can be find by procedure: > Sort([ p[1] : p in IntegralPoints(EllipticCurve([0, 1689])) ]); > but these procedure work only for b=0 > > BEST WISHES > ARTUR JASINSKI > > > >