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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Kyiv City MO
2021 Kyiv City MO
2021 Kyiv City MO Round 1
10.5
10.5
Part of
2021 Kyiv City MO Round 1
Problems
(1)
Largest power of $3$ dividing a_101
Source: Kyiv City MO 2021 Round 1, Problem 10.5
12/21/2023
The sequence
(
a
n
)
(a_n)
(
a
n
)
is such that
a
n
+
1
=
(
a
n
)
n
+
n
+
1
a_{n+1} = (a_n)^n + n + 1
a
n
+
1
=
(
a
n
)
n
+
n
+
1
for all positive integers
n
n
n
, where
a
1
a_1
a
1
is some positive integer. Let
k
k
k
be the greatest power of
3
3
3
by which
a
101
a_{101}
a
101
is divisible. Find all possible values of
k
k
k
.Proposed by Kyrylo Holodnov
number theory
Sequence