IMO 2009 #1 July 18, 2009Posted by Martin Camacho in Problem-solving, Uncategorized.
Tags: imo, number theory
The 2009 IMO was a few days ago – in this post I tackle what I think is one of the easier IMO problems, IMO 2009 #1.
The question is as follows:
Let be a positive integer and let () be distinct integers in the set such that divides for . Prove that does not divide .
For all , , . Then
Now, suppose . Then .
But and , so , a contradiction.
Very cool problem.