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2003 AIME I Question 14

AIME · 2003 AIME I

Question 14

The decimal representation of $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers and $m \lt n,$ contains the digits $2,$ $5,$ and $1$ consecutively, and in that order. Find the smallest value of $n$ for which this is possible.