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Bosnia and Herzegovina IMO TST
2022 Bosnia and Herzegovina IMO TST
3
3
Part of
2022 Bosnia and Herzegovina IMO TST
Problems
(1)
Bosnia and Herzegovina 2022 IMO TST P3
Source:
5/22/2022
An infinite sequence is given by
x
1
=
2
,
x
2
=
7
,
x
n
+
1
=
4
x
n
−
x
n
−
1
x_1=2, x_2=7, x_{n+1} = 4x_n - x_{n-1}
x
1
=
2
,
x
2
=
7
,
x
n
+
1
=
4
x
n
−
x
n
−
1
for all
n
≥
2
n \geq 2
n
≥
2
. Does there exist a perfect square in this sequence? [hide="Remark"]During the test the initial value of
x
1
x_1
x
1
was given as
1
1
1
, thus the problem was not graded
Sequence
algebra