Difference between revisions of "2006 Romanian NMO Problems/Grade 7/Problem 4"
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Revision as of 09:03, 28 July 2006
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