IMO 1977 SL 11

Origin: NET

Problem

Let n be an integer greater than 1. Define x1 = n, y1 = 1, xi+1 = xi + yi , yi+1 = n xi+1 for i = 1, 2, . . ., where [z] denotes the largest integer less than or equal to z. Prove that min{x1, x2, . . . xn} = [\sqrtn].