a/b + b/c + c/a = n

[all at abouthugo.de]

The following was posted on sci.math:

Dave Rusin wrote:
> 
[...]
> 
> The behaviour for all the values of n < 67 mentioned in the previous post
> follows the pattern of one of the preceding paragraphs, except that
> I was unable to verify that there were no solutions when n=62 and n=64
> (I suppose the ranks are one but my software found no generator for the
> curves in the little time I allotted, so I couldn't check to see whether
> the generator lay on the bounded part of the curve or not.)
> 
> dave

Subject: Re: a/b+b/c+c/a=n
Author: Allan MacLeod <allan.macleod at paisley.ac.uk> 
Date Posted: Jul 18 2003 8:26:40:000AM
The problem of the representation

N = a/b + b/c + c/a

with a,b,c integers ( not necessarily positive )
is discussed in the paper

TWO MORE REPRESENTATION PROBLEMS
by Andrew Bremner and Richard Guy
published in Proc. Edinburgh Math. Soc. vol 40 1997 pp 1-17.

N = 62 and N = 64 both have solutions but they are quite large.

Allan MacLeod