# 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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