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Topic: ---- --- ---- conditions for integer solutions
Replies: 15   Last Post: Dec 17, 2010 7:48 PM

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alainverghote@gmail.com

Posts: 812
Registered: 5/31/08
Re: ---- --- ---- conditions for integer solutions
Posted: Dec 16, 2010 5:05 AM
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On 16 déc, 07:17, Ulrich D i e z <eu_angel...@web.de> wrote:
> Ulrich D i e z wrote:
>
>
>

> > If you can write ek^2 with k a prime > 3 as
> > a product 4*s^2*t^2 , s > t > 0, gcd(s,t)=1, s =/= t (mod 2) ,

> [...]
> > Thus you can e.g. choose:
> > t : = k ;  k  a prime > 3 ;
> > s : = (k+1)  

> [...]
> > [instead of s : = (k+1) you could as well choose
> > s : = (k+m) with gcd(k,m) = 1... ]

>
> s : = (k+m) with gcd(k,m) = 1, m = 1 (mod 2)... ]
>
> Sorry, I don't know whether I was thinking at all.
>
> Ulrich


Bonjour,

It seems to me that all numerical solutions you gave
correspond to
(e/4+k^2)^2 = (e/4-k^2)^2+e*k^2
x^2 = y^2 + e*k^2
add one e=16 , k =7
53^3 = 45^2 +16*7^2 ,

With e/4 even.

Alain




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