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Estonian Math Competitions 2005/2006

Source: Final Round Grade 12 Pro 3

July 30, 2008
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Prove or disprove the following statements. a) For every integer n≥3 n \ge 3, there exist n n pairwise distinct positive integers such that the product of any two of them is divisible by the sum of the remaining n \minus{} 2 numbers. b) For some integer n≥3 n \ge 3, there exist n n pairwise distinct positive integers, such that the sum of any n \minus{} 2 of them is divisible by the product of the remaining two numbers.
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