UZ-MO 2011 Problem 2

Prove that $\forall n\in\mathbb{N}$ , $\exists a,b,c\in$ $\bigcup_{k\in\mathbb{N}}(k^{2},k^{2}+k+3\sqrt 3)$ such that $n=\frac{ab}{c}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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