Problem

Source: Bundeswettbewerb Mathematik 2015 - Round 2 - #2

Tags: number theory, Fraction, decimal representation



In the decimal expansion of a fraction $\frac{m}{n}$ with positive integers $m$ and $n$ you can find a string of numbers $7143$ after the comma. Show $n>1250$. Example: I mean something like $0.7143$.