2006 Romanian NMO Problems/Grade 7/Problem 4
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Problem
Let 
be a set of positive integers with at least 2 elements. It is given that for any numbers 
, 
we have 
, where by 
we have denoted the least common multiple of 
and 
. Prove that the set has exactly two elements.
Marius Gherghu, Slatina
Solution
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