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Let f(x)=x3+ax2+bx+cf(x) = x^3 + ax^2 + bx + cf(x)=x3+ax2+bx+c, where a,ba, ba,b, and ccc are real numbers. In order for f(x)f(x)f(x) to be invertible, aaa and bbb must be related as: ambn≤p\dfrac{a^m}{b^n} \leq p bnam≤p, where m,nm, nm,n, and ppp are also real numbers.
Find the mimimum value of m+n+pm + n + pm+n+p.
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