Level pending

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.

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