# Victor's Level 5 Challenges - 2

Let the three sides of a triangle be integers $$l,m,n$$ with $$l>m>n$$ and satisfy the equation

$\large \left\{\frac{3^l}{10^4}\right\}=\left\{\frac{3^m}{10^4}\right\}=\left\{\frac{3^n}{10^4}\right\}$

Find the minimum perimeter of such a triangle.

Details and Assumptions:

$$\{x\}=x-\left[x\right]$$ and $$\left[x\right]$$ denotes the integral part of the number $$x$$.

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