# Shifting the numbers, part 4

**Logic**Level 5

\[\frac{\overline{A_1A_2A_3\ldots A_{n-1}A_n}}{\overline{A_3\ldots A_{n-1}A_nA_1A_2}}=\frac{12}{17}\]

What is the smallest value of \(n>6\) such that there exist solutions to the above equation?

**Remark**: \(\overline{A_1A_2A_3\ldots A_{n-1}A_n}\) is a \(n\)-digit number. When \(n=6\), there exist solutions to the above equation. Try it!

This question is part of the set Shifting the numbers.