From: NoJunkMail@this.address (Gerry Myerson)
Newsgroups: sci.math
Subject: Re: 3^x+5^y=7^z+1
Date: Thu, 05 Feb 1998 11:12:59 +1100
In article <34d86bb2.1778879@news.nettuno.it>, spalland@comune.re.it
(Andrea Spallanzani) wrote:
> What are the solutions of the equation
>
> 3^x+5^y=7^z+1 ?
>
> (x,y,z positive integers)
I don't know.
This is the kind of problem that is solved in J L Brenner & L L Foster,
Exponential diophantine equations, Pacific J Math 101 (1982) 263--301,
MR 83k:10035. There are some other papers by one or the other of those
authors, and/or L J Alex. It might be most efficient to do a search of
Math Reviews for "exponential diophantine equations."
Then again, there may be some really simple congruence/divisibility
arguments that show that (1, 1, 1) is the only solution.
Gerry Myerson (gerry@mpce.mq.edu.au)