Belorusija, 2012

Geometry Difficulty 4.8 AIME Prove it Belarus

Let $m$ , $n$ , $k$ be pairwise relatively prime positive integers greater than $3$ .
Find the minimal possible number of points on the plane with the following property: there are $x$ of them which are the vertices of a regular $x$ -gon for $x = m$ , $x = n$ , $x = k$ .

Solution

Answer: $m + n + k - 4$ .

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