IMO 2009 Shortlist C3
Let n be a positive integer. Given a sequence ε1,...,εn−1 with εi = 0 or εi = 1 for each i = 1,...,n − 1, the sequences ...
Category: Combinatorics
Problem
Let n be a positive integer. Given a sequence ε1,...,εn−1 with εi = 0 or εi = 1 for each i = 1,...,n − 1, the sequences a0,...,an and b0,...,bn are constructed by the following rules: a0 = b0 = 1, a1 = b1 = 7, ai+1 = ( 2ai−1 + 3ai, if εi = 0, 3ai−1 + ai, if εi = 1, for each i = 1,...,n − 1, bi+1 = ( 2bi−1 + 3bi, if εn−i = 0, 3bi−1 + bi, if εn−i = 1, for each i = 1,...,n − 1. Prove that an = bn.