MathDB
Let sequence

Source: Balkan MO 2002, problem 2

February 2, 2006
inductionalgebrabinomial theoremalgebra solved

Problem Statement

Let the sequence {an}n≥1 \{a_n\}_{n\geq 1} be defined by a_1 \equal{} 20, a_2 \equal{} 30 and a_{n \plus{} 2} \equal{} 3a_{n \plus{} 1} \minus{} a_n for all n≥1 n\geq 1. Find all positive integers n n such that 1 \plus{} 5a_n a_{n \plus{} 1} is a perfect square.
Back to ProblemsView on AoPS