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EGMO 2015 Hari 2 Soal 4.

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Tentukan apakah terdapat barisan tak-hingga bilangan asli $a_1, a_2, \cdots$ yang memenuhi relasi

\[a_{n+2} = a_{n+1} + \sqrt{a_{n+1} + a_n}  \]

untuk setiap bilangan asli $n$.

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