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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