Problem

Source: Federation of Bosnia, 1. Grades 2008.

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Given are two disjoint sets $ A$ and $ B$ such that their union is $ \mathbb N$. Prove that for all positive integers $ n$ there exist different numbers $ a$ and $ b$, both greater than $ n$, such that either $ \{ a,b,a + b \}$ is contained in $ A$ or $ \{ a,b,a + b \}$ is contained in $ B$.