MathDB

For a set

A

, we define

A + A = \{a + b: a, b \in A \}

. Determine whether there exists a set

A

of positive integers such that \sum_{a \in A} \frac{1}{a} = +\infty \text{and} \lim_{n \rightarrow +\infty} \frac{|(A+A) \cap \{1,2,\cdots,n \}|}{n}=0.
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Problem Statement