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\frac{43}{197} < \frac { \alpha }{ \beta } < \frac{17}{77}

Source: INMO 2005 Problem 2

August 23, 2005
number theory unsolvednumber theory

Problem Statement

Let α\alpha and β\beta be positive integers such that 43197<αβ<1777\dfrac{43}{197} < \dfrac{ \alpha }{ \beta } < \dfrac{17}{77}. Find the minimum possible value of β\beta.
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