Re: Integral points on elliptic curves

• To: mathgroup at smc.vnet.net
• Subject: [mg122364] Re: Integral points on elliptic curves
• From: Costa Bravo <q13a27tt at aol.com>
• Date: Wed, 26 Oct 2011 17:40:36 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j80q8p\$adb\$1@smc.vnet.net> <j862sg\$5v7\$1@smc.vnet.net>

```  Emu write:
>>
>> FindInstance[y^3 - x^2 == 1641843, {x, y}, Integers]
>>
>> if FindInstance doesn't work what inspite???
>>

> 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[51]:= AbsoluteTiming[
Cases[Join @@  Table[{x, y, y^3 - x^2 == 1641843}, {x, 1, 1000}, {y, 1,
1000}], {__, True}]]

Out[51]= {4.6718750, {{468, 123, True}}}

better

In[60]:= k = 1641843;
AbsoluteTiming[y0 = Ceiling[k^(1/3)];
Do[If[FractionalPart[Sqrt[y^3 - k]] == 0,Print[Sqrt[y^3 - k], "  ", y]], {y, y0, 10000}]]

468  123
11754  519

Out[61]= {3.4375000, Null}

--
Costa

```

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