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Saudi Arabia Contests
Saudi Arabia JBMO TST
2021 Saudi Arabia JBMO TST
1
1
Part of
2021 Saudi Arabia JBMO TST
Problems
(1)
a_n = a^2_{n-1} + 15a_{n-1} has no perfect squares
Source: 2021 Saudi Arabia JBMO TST 2.1
9/4/2021
Let
(
a
n
)
n
≥
1
(a_n)_{n\ge 1}
(
a
n
)
n
≥
1
be a sequence given by
a
1
=
45
a_1 = 45
a
1
=
45
and
a
n
=
a
n
−
1
2
+
15
a
n
−
1
a_n = a^2_{n-1} + 15a_{n-1}
a
n
=
a
n
−
1
2
+
15
a
n
−
1
for
n
>
1
n > 1
n
>
1
. Prove that the sequence contains no perfect squares.
number theory
recurrence relation