The least positive value of the parameter \( a \) for which there exists atleast one line that i...

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The least positive value of the parameter \( a \) for which there exists atleast one line that is tangent to the graph of the curve \( y=x^{3}-a x \), at one point and normal to the graph at another point is \( \frac{p}{q} \); where \( p \) and \( q \) are relatively prime positive integers. Find product \( p q \).
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