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

Author: Vjekoslav Kovač, Croatia

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