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find the greatest n

Source: ItaMO 2005, P4

March 9, 2012
number theory proposednumber theory

Problem Statement

Determine all n≥3n \geq 3 for which there are nn positive integers a1,⋯ ,ana_1, \cdots , a_n any two of which have a common divisor greater than 11, but any three of which are coprime. Assuming that, moreover, the numbers aia_i are less than 50005000, find the greatest possible nn.
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