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An easy problem from Irish Mathematical Olympiad

Source: Irish Mathematical Olympiad 2014,P6

March 13, 2016
number theory

Problem Statement

Each of the four positive integers N,N+1,N+2,N+3N,N +1,N +2,N +3 has exactly six positive divisors. There are exactly20 20 di erent positive numbers which are exact divisors of at least one of the numbers. One of these is 2727. Find all possible values of NN.(Both 11 and mm are counted as divisors of the number mm.)
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