Problem #57
Smallest Perimeter
The sides of a triangle have integer lengths k, m and n.
Assume that k >m > n and \{\frac{3^k}{10^4}\}=\{\frac{3^m}{10^4}\}=\{\frac{3^n}{10^4}\}.
where \{x\} denotes the fractional part of a number.
Determine the minimum value of the perimeter of the triangle.