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a_1 = 1, a_{n+2} = 2a_{n+1} - a_n +2 , a_na_{n+1} = a_m

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p5

February 17, 2020
recurrence relationSequencealgebra

Problem Statement

A sequence of natural numbers a1,a2,...a_1,a_2,... satisfies a1=1,an+2=2an+1−an+2a_1 = 1, a_{n+2} = 2a_{n+1} - a_n +2 for n∈Nn \in N. Prove that for every natural nn there exists a natural mm such that anan+1=ama_na_{n+1} = a_m.
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