IMO 2007 Shortlist A5
Let c > 2, and let a(1),a(2),... be a sequence of nonnegative real numbers such that a(m + n) ≤ 2a(m) + 2a(n) for all m,...
Category: Algebra
Problem
Let c > 2, and let a(1),a(2),... be a sequence of nonnegative real numbers such that a(m + n) ≤ 2a(m) + 2a(n) for all m,n ≥ 1, (1) and a(2k ) ≤ (k + 1)c for all k ≥ 0. (2) Prove that the sequence a(n) is bounded. (Croatia)