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Given positive reals a,b,ca,b,ca,b,c such that a+b+c=abca+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)}(a2+1)(b2+1)(c2+1) is mmm. Find the value of ⌊100m⌋\lfloor 100m\rfloor⌊100m⌋.
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