Sum is Product Inequality

Algebra Level 3

Given positive reals a,b,ca,b,c such that a+b+c=abca+b+c=abc then the minimum value of (a2+1)(b2+1)(c2+1)\sqrt{(a^2+1)(b^2+1)(c^2+1)} is mm. Find the value of 100m\lfloor 100m\rfloor.

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