How many integer solutions for $a$ and $b$ in $(ab)/(a+b)=3600$?
My attempt:
$(ab)/(a+b)=3600$
= $ab=3600(a+b)$
= $ab=3600a+3600b$
=$ab=3600a=3600b$
Dividing $3600b$ on both sides
=$a(1-3600)/3600$
I am not really sure if this is correct. I was just doing this for fun after I was reading this in some mathematical book. It just explained about a few things not much. Can someone please help me with this? I was trying this for a while now and wanted to know what it would look like.
HINT : Note that $$\begin{align}\frac{ab}{a+b}=3600&\iff ab=3600(a+b)\ \ \text{and}\ \ a+b\not=0\\&\iff (a-3600)(b-3600)=3600^2\ \ \text{and}\ \ a+b\not=0.\end{align}$$ Can you take it from here?