# Minimum Perimeter

A triangle has all its sides as integers marked l,m,n with l>m>n.

Also given that \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 the triangle.

{} denotes the fractional part.

21
Shubhodip ·

What meets the eye at first look is 3^{l}\equiv 3^{m}\left ( mod 10^{4} \right ) and 3^{m}\equiv 3^{n}\left ( mod 10^{4} \right )

After this it should be solvable but i think i need more time.

21
Shubhodip ·

I have seen the solution. knew something i did not:)