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Let

\{a_k\}_{k\geq 1}

be a sequence of non-negative integers, such that

a_k \geq a_{2k} + a_{2k+1}

, for all

k\geq 1

. a) Prove that for all positive integers

n\geq 1

there exist

n

consecutive terms equal with 0 in the sequence

\{a_k\}_k

; b) State an example of sequence with the property in the hypothesis which contains an infinite number of non-zero terms.

Problem Statement