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)