MathDB
a(m+n) >= 2 a(m) + 2 a(n) for all m,n >= 1

Source: IMO Shortlist 2007, A5

July 13, 2008
inequalitiesSequenceboundedrecurrence relationIMO Shortlist

Problem Statement

Let c>2, c > 2, and let a(1),a(2),… a(1), a(2), \ldots be a sequence of nonnegative real numbers such that a(m \plus{} n) \leq 2 \cdot a(m) \plus{} 2 \cdot a(n) \text{ for all } m,n \geq 1, and a\left(2^k \right) \leq \frac {1}{(k \plus{} 1)^c} \text{ for all } k \geq 0. Prove that the sequence a(n) a(n) is bounded. Author: Vjekoslav Kovač, Croatia
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