I have a question:
How many triples $(a,b,c)$ are there such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} = 1$ and $a ? They have to be positive integers. Also find those triples.
I know that all of them have to be $\geq 2$. So do I just fix a number and count the other pairs?
If I choose $a = 3$ then I count the other pairs $(b,c)$? If I choose a very large $a$ then it seems that no triples will satisfy the condition since the sum will be too small.