MathDB
g(n+2) = g(n) + g(n+1) + 1

Source: IMO LongList 1988, Ireland 4, Problem 45 of ILL

November 3, 2005
quadraticsnumber theory unsolvednumber theory

Problem Statement

Let g(n)g(n) be defined as follows: g(1)=0,g(2)=1 g(1) = 0, g(2) = 1 and g(n+2)=g(n)+g(n+1)+1,n≥1. g(n+2) = g(n) + g(n+1) + 1, n \geq 1. Prove that if n>5n > 5 is a prime, then nn divides g(n)⋅(g(n)+1).g(n) \cdot (g(n) + 1).
Back to ProblemsView on AoPS