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2015 Azerbaijan IMO TST

Source: 2015 Azerbaijan IMO TST

May 29, 2015
Combinatorial Number Theorycombinatorics

Problem Statement

We say that AA=={a1,a2,a3⋯ana_1,a_2,a_3\cdots a_n} consisting n>2n>2 distinct positive integers is goodgood if for every i=1,2,3⋯ni=1,2,3\cdots n the number ai2015{a_i}^{2015} is divisible by the product of all numbers in AA except aia_i. Find all integers n>2n>2 such that exists a goodgood set consisting of nn positive integers.
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