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Barisan tambah/kurang

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Cari semua barisan $a_0, a_1, a_2, \dotsc$ di bilangan bulat positif dengan $a_0 \ge 2015$ sehingga untuk setiap $n \in \mathbb{N}$:

(i) $a_{n+2}$ habis dibagi $a_n$, dan

(ii) $|s_{n+1}-(n+1)a_n|=1$ dengan $s_{n+1}=a_{n+1}-a_n+a_{n-1}-\dotsb +(-1)^{n+1}a_0$.


APMO 2015 no. 5 oleh Pakawut Jiradilok dan Warut Suksompong, Thaliand

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