Problem #PRU-110212

Problems Methods Real numbers Integer and fractional parts. Archimedean property Pigeonhole principle (angles and lengths) Pigeonhole principle Calculus
 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?