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IMO 2009 #1 *July 18, 2009*

*Posted by Martin Camacho in Problem-solving, Uncategorized.*

Tags: imo, number theory

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Tags: imo, number theory

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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 .

**My solution**

For all , , . Then

.

Now, suppose . Then .

But and , so , a contradiction.

Very cool problem.

[...] 证法二：Martin Camacho提到另一个方法，如下： [...]

My solution is almost similar. There can be other variations to this problem too.