Competition problem — Number theory

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Number theory Difficulty 4.7 AIME Prove it Soviet Union

Problem:

Show that there are infinitely many triples of distinct positive integers $a$ , $b$ , $c$ such that each divides the product of the other two and $a + b = c + 1$ .

Solution

Solution:

$\{ n(n + 1),\ n(n^2 + n - 1),\ (n + 1)(n^2 + n - 1) \}$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.