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2006 Romanian NMO Problems/Grade 7/Problem 4

Revision as of 07:32, 27 August 2008 by 1=2 (talk | contribs) (→‎Solution)

Problem

Let $A$ be a set of positive integers with at least 2 elements. It is given that for any numbers $a>b$, $a,b \in A$ we have $\frac{ [a,b] }{ a- b } \in A$, where by $[a,b]$ we have denoted the least common multiple of $a$ and $b$. Prove that the set $A$ has exactly two elements.

Marius Gherghu, Slatina

Solution

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See also

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