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MathGroup Archive 2006

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Re: Re: Demostration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70465] Re: [mg70453] Re: [mg70369] Demostration
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Tue, 17 Oct 2006 02:58:32 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

The second test in Select is unnecessary. This should have been

Select[Flatten[ 
    Table[{{x, -Sqrt[x^3 + 9]}, {x, Sqrt[x^3 + 9]}}, 
      {x, -2, 500}], 1], 
  IntegerQ[#[[2]]] &]


Bob Hanlon

---- Bob Hanlon <hanlonr at cox.net> wrote: 
> Reduce[{y^2==x^3+9}, {x,y},Integers]
> 
> (x | y) âË?Ë? Integers && x >= -2 && 
>   (y == -Sqrt[x^3 + 9] || y == Sqrt[x^3 + 9])
> 
> Select[Flatten[
>     Table[{{x,-Sqrt[x^3+9]},{x,Sqrt[x^3+9]}},
>       {x,-2,500}],1],
>   IntegerQ[#[[2]]]&&#[[2]]^2==#[[1]]^3+9&]
> 
> {{-2, -1}, {-2, 1}, {0, -3}, {0, 3}, {3, -6}, {3, 6}, 
>   {6, -15}, {6, 15}, {40, -253}, {40, 253}}
> 
> Length[%]
> 
> 10
> 
> 
> Bob Hanlon
> 
> ---- Miguel <mibelair at hotmail.com> wrote: 
> > How canI to demostrate than the equation y^2=x^3+9 has 10 integer
> > solutions?
> > 
> 
> --
> 
> Bob Hanlon
> hanlonr at cox.net
> 
> 

--

Bob Hanlon
hanlonr at cox.net



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