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International Contests
EGMO
2020 EGMO
6
6
Part of
2020 EGMO
Problems
(1)
2020 EGMO P6: m such that 3-term linear recurrence is always a square
Source: 2020 EGMO P6
4/18/2020
Let
m
>
1
m > 1
m
>
1
be an integer. A sequence
a
1
,
a
2
,
a
3
,
…
a_1, a_2, a_3, \ldots
a
1
,
a
2
,
a
3
,
…
is defined by
a
1
=
a
2
=
1
a_1 = a_2 = 1
a
1
=
a
2
=
1
,
a
3
=
4
a_3 = 4
a
3
=
4
, and for all
n
≥
4
n \ge 4
n
≥
4
,
a
n
=
m
(
a
n
−
1
+
a
n
−
2
)
−
a
n
−
3
.
a_n = m(a_{n - 1} + a_{n - 2}) - a_{n - 3}.
a
n
=
m
(
a
n
−
1
+
a
n
−
2
)
−
a
n
−
3
.
Determine all integers
m
m
m
such that every term of the sequence is a square.
EGMO 2020
Sequence
Perfect Squares
EGMO