## Problem #022 - coprimes in the crowd

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This simple problem is an example of a very interesting phenomenon: if you have a large enough "universe" to consider, even randomly picked parts exhibit structured properties.

### Problem statement

Let $$n \geq 2$$ be an integer. Then, consider the integers

$\{3, 4, \cdots, 2n-1, 2n\}\ .$

Show that, if you pick $$n$$ from those, you always have two numbers that will share no divisors whatsoever.

In other words, show that there's two of those $$n$$ numbers that are coprime.

If you need any clarification whatsoever, feel free to ask in the comment section below.