# Sum of roots over each other

Level pending

Given that $$p$$ and $$q$$ are prime numbers and they are the roots of the quadratic equation

$x^2-61x+m=0$

where $$m$$ is a constant. Then, $$\frac{p}{q}+\frac{q}{p}=\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. What are the last 3 digits of $$a+b$$?

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