MathDB

Integer sequence

Source: 2009 AIME I #13

March 18, 2009

inductionmodular arithmeticinequalitiesarticlespigeonhole principlefunctionAMC

Problem Statement

The terms of the sequence

(a_i)

defined by a_{n \plus{} 2} \equal{} \frac {a_n \plus{} 2009} {1 \plus{} a_{n \plus{} 1}} for

n \ge 1

are positive integers. Find the minimum possible value of a_1 \plus{} a_2.