# 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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