Will that be a small triangle?

Let the three sides of a triangle be integers \(a,b,c\) respectively, satisfying \(a > b > c\) and \( f\left (\frac{3^a}{10^4}\right)=f\left (\frac{3^b}{10^4}\right)=f\left(\frac{3^c}{10^4}\right)\) where \(f(x)=x-\lfloor x \rfloor\). Find the minimum perimeter of such a triangle.

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