Editorial for COCI '06 Contest 4 #3 Prsteni


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The number of times the i^{th} ring turns depends only on its radius and the radius of the first ring. The sought ratio is R_i / R_1. Reducing the fractions can be done by dividing the numerator and denominator by their greatest common divisor, given by the recursive formula:

\displaystyle \gcd(a,b) = \begin{cases}a & \text{when }b=0 \\ \gcd(b, a \bmod b) & \text{when }b \ne 0\end{cases}


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