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Caucasus Mathematical Olympiad
2020 Caucasus Mathematical Olympiad
3
3
Part of
2020 Caucasus Mathematical Olympiad
Problems
(1)
No perfect squares in a_n=a_{n-1}^2+6a_{n-1}
Source: 2020 Caucasus Mathematical Olympiad
3/16/2020
Let
a
n
a_n
a
n
be a sequence given by
a
1
=
18
a_1 = 18
a
1
=
18
, and
a
n
=
a
n
−
1
2
+
6
a
n
−
1
a_n = a_{n-1}^2+6a_{n-1}
a
n
=
a
n
−
1
2
+
6
a
n
−
1
, for
n
>
1
n>1
n
>
1
. Prove that this sequence contains no perfect powers.
number theory
algebra
Sequence