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)