[seqfan] Re: Diophantine 4+5x^3=y^2

[Max Alekseyev]

Zak,

Multiplying by 5^2 and making substitution
x' = 5x, y' = 5y
we got a Mordell curve: y'^2 = x'^3 + 100
for which we can query http://tnt.math.metro-u.ac.jp/simath/MORDELL/

We are interested in solutions divisible by 5, and up to a sign there
are only 4 of them.
So, your list is complete.

Regards,
Max

On Fri, Dec 5, 2008 at 8:51 AM, zak seidov <zakseidov at yahoo.com> wrote:
> Dear SeqFans,
>
> Diophantine 4+5x^3=y^2 has 4 solutions (x,y >= 0):
> x=0,1,4,532 and y=2,3,18,27438.
> Are there more solutions (x>2*10^9)?
> thx, zak
>
> (17:59) gp > {for(x=0,2*10^9,if(issquare(4+5* x^3,&y),print(x","y)))}
> 0,2
> 1,3
> 4,18
> 532,27438
> (18:46) gp >
>
>
>
>
>
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