2013 OIM Problems/Problem 1
Problem
A set of positive integers is called "canalero" if for any three numbers , all different, it holds that divides , divides , and divides .
1. Show that, for any finite set of positive integers , there exist infinite positive integers such that the set is a canalero.
2. Show that, for any integer , there is a canalero set that has exactly elements and no integer greater than 1 divides all its elements.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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