An application of the pigeon hole principle

Question

I'm interested in a reference (preferably the original source) of the following result which can be proven using the pigeon hole principle:

Let $K$ be a subset of $\{1,...,2n\}$ with $|K| \geq n+1$. Then there are $k,l \in K$ such that $k$ is a proper divisor of $l$.

Are there any generalizations?

Answer 1

I found this link from Cut-The-Knot with two references:

1. B. Bollobás, The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press, 2006, p. 48.

2. I. F. Sharygin, Mathematical Mosaic, Mir, 2002, problem 65.3 (in Russian)