Originally Posted by

**tonio** I think that's a very nice and promising way to approach it. About "duplicate" I think Chip's idea may be right. For example,

for $\displaystyle \displaystyle{n=6\,,\,\frac{1}{x}+\frac{1}{y}=\fra c{1}{6}\Longleftrightarrow (x-6)(y-6)=36}$ . We have here

the solutions $\displaystyle (9,18), (18,9)$ , and these are, perhaps, called "duplicate". I'd rather call the solutions "different up to order of x,y" ,

but as long as the idea is clear...

In the above example, we've the solutions $\displaystyle (42,7), (24,8), (18,9),(15,10),(12,12,)$ , 5 different

(up to order) solutions, but I am not able to apply the "duplicate" thingy a priori, i.e. before I know

the solutions...

Tonio