Re: Integral points on elliptic curves

*To*: mathgroup at smc.vnet.net*Subject*: [mg122335] Re: Integral points on elliptic curves*From*: Emu <samuel.thomas.blake at gmail.com>*Date*: Tue, 25 Oct 2011 06:19:21 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <j80q8p$adb$1@smc.vnet.net>

On Oct 23, 9:28 pm, Artur <gra... at csl.pl> wrote: > Dear Mathematica Gurus, > Who know that existed any Mathematica procedure (library) to finding > integral points on elliptic curves? > Or how to find example to e.g. > > FindInstance[y^3 - x^2 == 1641843, {x, y}, Integers] > > if FindInstance doesn't work what inspite??? > > Unfortunatelly Wolfram Research is developing some branches of > Mathematics in new versions of Mathematica and complete leave anothers > (good samples are elliptic curves, Chabauty method, determining Galois > groups of polynomials etc.). > > Best wishes > Artur Jasinski How about something as naive as In[31]:= Cases[Join @@ Table[{x, y, y^3 - x^2 == 1641843}, {x, 1, 1000}, {y, 1, 1000}], {__, True}] Out[31]= {{468, 123, True}} In[32]:= 123^3 - 468^2 == 1641843 Out[32]= True Sam Blake