MathDB
Many square roots, but rational !

Source: Balkan Olympiad 2007,problem 3

April 28, 2007
algebrapolynomialfloor functioninductionnumber theory unsolvednumber theory

Problem Statement

Find all positive integers nn such that there exist a permutation σ\sigma on the set {1,2,3,…,n}\{1,2,3, \ldots, n\} for which σ(1)+σ(2)+…+σ(n−1)+σ(n)\sqrt{\sigma(1)+\sqrt{\sigma(2)+\sqrt{\ldots+\sqrt{\sigma(n-1)+\sqrt{\sigma(n)}}}}} is a rational number.
Back to ProblemsView on AoPS