Straightforward a little please

There are $N$ ordered triplets $(a,b,c)$ satisfy

$\Big(\frac{a}{b}\Big)^2+1=\Big(\frac{c}{b}\Big)^2$

What is the last three digits of $N$ if $0<a,b,c<1000$ ?

Details and Assumptions

All the fractions are in the lowest terms.