# 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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