non-negative elements
Source: Bundeswettbewerb Mathematik 1991, round two, problem 4
June 19, 2004
algebra unsolvedalgebra
Problem Statement
Given wo non-negative integers and , one of them is odd and the other one even. By the following rule we define two sequences :
a_0 = a, a_1 = b, a_{n+1} = 2a_n - a_{n-1} + 2 (n = 1,2,3, \ldots)
b_0 = b, b_1 = a, b_{n+1} = 2a_n - b_{n-1} + 2 (n = 1,2,3, \ldots)
Prove that none of these two sequences contain a negative element if and only if we have .