Problem

Source:

Tags: induction, modular arithmetic, number theory, combinatorics proposed, combinatorics



Let $ A$ be the subset of the set of positive integers, having the following $ 2$ properties: 1) If $ a$ belong to $ A$,than all of the divisors of $ a$ also belong to $ A$; 2) If $ a$ and $ b$, $ 1 < a < b$, belong to $ A$, than $ 1 + ab$ is also in $ A$; Prove that if $ A$ contains at least $ 3$ positive integers, than $ A$ contains all positive integers.