An algebra problem by Darel Gunawan

Algebra Level 5

Given that \(a,b\) and \(c\) are positive numbers such that \( \dfrac{ab+1}{3b} = \dfrac{bc+1}{4c} = \dfrac{ac+ 1}{5a} \) is a prime number. Find the minimum value of \( abc +\dfrac1{abc} \).

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