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RU-ALLRUSSIAN 1982 Problem 2
The sequence a n \mathbf{a}_{\mathrm{n}} a n is defined by a 1 = 1 \mathbf{a}_{1} = 1 a 1 = 1 , a 2 = 2 \mathbf{a}_{2} = 2 a 2 = 2 , a n + 2 = a n + 1 + a n \mathbf{a}_{\mathrm{n} + 2} = \mathbf{a}_{\mathrm{n} + 1} + \mathbf{a}_{\mathrm{n}} a n + 2 = a n + 1 + a n . The sequence b n \mathbf{b}_{\mathrm{n}} b n is defined by b 1 = 2 \mathbf{b}_{1} = 2 b 1 = 2 , b 2 = 1 \mathbf{b}_{2} = 1 b 2 = 1 , b n + 2 = b n + 1 + b n \mathbf{b}_{\mathrm{n} + 2} = \mathbf{b}_{\mathrm{n} + 1} + \mathbf{b}_{\mathrm{n}} b n + 2 = b n + 1 + b n . How many integers belong to both sequences?
Dataset text NuminaMath olympiads . Quoted with source.
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