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RU-ALLRUSSIAN 1982 Problem 2

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The sequence an\mathbf{a}_{\mathrm{n}} is defined by a1=1\mathbf{a}_{1} = 1 , a2=2\mathbf{a}_{2} = 2 , an+2=an+1+an\mathbf{a}_{\mathrm{n} + 2} = \mathbf{a}_{\mathrm{n} + 1} + \mathbf{a}_{\mathrm{n}} . The sequence bn\mathbf{b}_{\mathrm{n}} is defined by b1=2\mathbf{b}_{1} = 2 , b2=1\mathbf{b}_{2} = 1 , bn+2=bn+1+bn\mathbf{b}_{\mathrm{n} + 2} = \mathbf{b}_{\mathrm{n} + 1} + \mathbf{b}_{\mathrm{n}} . How many integers belong to both sequences?

Dataset text NuminaMath olympiads. Quoted with source.

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1,2,3

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