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2019 Greece National Olympiad
1
2019 Greece National Olympiad Q1
2019 Greece National Olympiad Q1
Source: 2019 Greece National Olympiad
March 11, 2019
number theory
Problem Statement
Define the sequnce
(
a
n
)
n
≥
1
{(a_n)}_{n\ge1}
(
a
n
)
n
≥
1
by
a
1
=
1
a_1=1
a
1
=
1
and
a
n
=
5
a
n
−
1
+
3
n
−
1
a_n=5a_{n-1}+3^{n-1}
a
n
=
5
a
n
−
1
+
3
n
−
1
for
n
≥
2
n\ge2
n
≥
2
. Find the greatest power of
2
2
2
that divides
a
2
2019
a_{2^{2019}}
a
2
2019
.
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