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

David Wilson dwilson at gambitcomm.com
Wed Nov 19 16:43:18 CET 2008

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
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