[seqfan] Re: Possible solutions of 3^x+5^y=2^z

[David Wilson]

But that's not your problem is it?

If you relayed the result correctly, then the Darmon and Granville paper 
would show that

    x^3 + y^5 = z^2

has a finite number of solutions under the dubious condition that 
1/3+1/5+1/2 < 1.

I don't see the connection to 3^x + 5^y = 2^z.


Artur wrote:
> Dear Seqfans,
> I was meet yesterday with one of the best World specialists from Number 
> Theory Prof. Andrzej Schonzel and ask them about number of possible 
> solutions of equation 3^x+5^y=2^z.
> My problem was formulated as conjuncture by Fermat and later 
> refolumlated on much genaral case by Catalan and was prooved by Darmon 
> and Granville in 1995 (Bull.London.Math.Society 27 pp.513-543) that each 
> Dipohantine equation type p^x+q^y=r^z and 1/x+1/y+1/z<1 have only finite 
> number of solutions. This article have many other very interesting ideas!
> Best wishes
> Artur
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>
>
>