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2006 positive integers and 2006 pairwise distinct fractions

Source: China NMO 2006, Problem 2

January 29, 2006

number theory unsolvednumber theory

Problem Statement

For positive integers

a_1,a_2 ,\ldots,a_{2006}

such that

\frac{a_1}{a_2},\frac{a_2}{a_3},\ldots,\frac{a_{2005}}{a_{2006}}

are pairwise distinct, find the minimum possible amount of distinct positive integers in the set

\{a_1,a_2,...,a_{2006}\}