Home Competitions RS-SMO 2019 Problem 6
Sequences ( a n ) n = 0 ∞ (a_n)_{n=0}^{\infty} ( a n ) n = 0 ∞ ( b n ) n = 0 ∞ (b_n)_{n=0}^{\infty} ( b n ) n = 0 ∞ a 0 = 0 , a 1 = 1 , a n + 1 = 2018 n a n + a n − 1 for n ≥ 1 a_0=0 , \;\; a_1=1, \;\;\; a_{n+1}=\frac{2018}{n} a_n+ a_{n-1}\;\; \text {for }\;\; n\geq 1 a 0 = 0 , a 1 = 1 , a n + 1 = n 2018 a n + a n − 1 for n ≥ 1 b 0 = 0 , b 1 = 1 , b n + 1 = 2020 n b n + b n − 1 for n ≥ 1 b_0=0 , \;\; b_1=1, \;\;\; b_{n+1}=\frac{2020}{n} b_n+ b_{n-1}\;\; \text {for }\;\; n\geq 1 b 0 = 0 , b 1 = 1 , b n + 1 = n 2020 b n + b n − 1 for n ≥ 1 a 1010 1010 = b 1009 1009 \frac{a_{1010}}{1010}=\frac{b_{1009}}{1009} 1010 a 1010 = 1009 b 1009
Dataset text AI-MO AoPS . Quoted with source.
Official text: Serbian Mathematical Olympiad 2019 official paper , page 2.
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