Problem #PRU-110212

Problems Calculus Real numbers Integer and fractional parts. Archimedean property Methods Pigeonhole principle Pigeonhole principle (angles and lengths)
 13–15  3.0

Problem

For what natural numbers \(n\) are there positive rational but not whole numbers \(a\) and \(b\), such that both \(a + b\) and \(a^n + b^n\) are integers?