# Shifting the numbers, part 5

**Number Theory**Level 5

\[\frac{\overline{A_1A_2A_3\ldots A_{n-1}A_n}}{\overline{A_2A_3\ldots A_{n-1}A_nA_1}}=\frac{12}{17}\]

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

**Remark**: You may try a related problem here.

This question is part of the set Shifting the numbers.