Library / All-Soviet-Union Mathematical Olympiad /38 of 185

All-Soviet-Union Mathematical Olympiad

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:

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

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

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