Problem

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Tags: number theory, 1st edition



Let $(A_i)_{i\ge 1}$ be sequence of sets of two integer numbers, such that no integer is contained in more than one $A_i$ and for every $A_i$ the sum of its elements is $i$. Prove that there are infinitely many values of $k$ for which one of the elements of $A_k$ is greater than $13k/7$.