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Number Theory

Source: 2003 National High School Mathematics League, Exam Two, Problem 2

March 16, 2020
number theory

Problem Statement

Let the lengths of three sides of a triangle be l,m,n(l>m>n)l, m, n(l>m>n). If {3l104}={3m104}={3n104}\left\{\frac{3^l}{10^4}\right\}=\left\{\frac{3^m}{10^4}\right\}=\left\{\frac{3^n}{10^4}\right\}, find the minimum value of the perimeter of the triangle. Note: {x}=x−[x]\{x\}=x-[x] and [x][x] denotes the integral part of number xx.
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