MathDB

Prove that, for any integer

a_{1}>1

, there exist an increasing sequence of positive integers

a_{1}, a_{2}, a_{3}, \cdots

such that

a_{1}+a_{2}+\cdots+a_{n}\; \vert \; a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}

for all

n \in \mathbb{N}

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