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a_{n+1} =(1989+a_na_{n-1})/a_{n-2}

Source: Romania IMO TST 1989 3.2

February 17, 2020

recurrence relationSequencenumber theoryalgebra

Problem Statement

The sequence (

a_n

) is defined by

a_1 = a_2 = 1, a_3 = 199

and

a_{n+1} =\frac{1989+a_na_{n-1}}{a_{n-2}}

for all

n \ge 3

. Prove that all terms of the sequence are positive integers