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Bosnia and Herzegovina 2022 IMO TST P3

Source:

May 22, 2022
Sequencealgebra

Problem Statement

An infinite sequence is given by x1=2,x2=7,xn+1=4xn−xn−1x_1=2, x_2=7, x_{n+1} = 4x_n - x_{n-1} for all n≥2n \geq 2. Does there exist a perfect square in this sequence? [hide="Remark"]During the test the initial value of x1x_1 was given as 11, thus the problem was not graded
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