Circular Numbers

Number Theory Level pending

Given a positive integer \(a\), let \(b\) be the integer formed by shifting the digits of \(a\) one decimal place to the left (and moving the first digit to the last - i.e. \(123\) becomes \(231\)) and \(c\) the integer formed by shifting the digits of \(b\) in a similar manner.

Find is the least integer \(a\) such that: \[\frac{b}{a} = \frac{c}{b} = \frac{3}{2}\]

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