[seqfan] Re: Possible solutions of 3^x+5^y=2^z
Artur
grafix at csl.pl
Wed Nov 19 09:19:20 CET 2008
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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