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Reverse Product

Author: mathforces
Problem has been solved: 36 times

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For some positive integer $ 2020> n> 2 $, the fractions $\frac{1}{2}$, $\frac{2}{3}$, $\frac{3}{4}$, ...,$\frac{n-1}{n}$. Find the number of all such $ n $ for which some of the fractions can be inverted (that is, replaced by the inverse) so that the product of all fractions becomes equal to one?

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