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2018 AIME Problems
2
Sequences Modulo 11: Indexblocked
Sequences Modulo 11: Indexblocked
Source: 2018 AIME II #2
March 23, 2018
abstract algebra
AMC
AIME
AIME II
Problem Statement
Let
a
0
=
2
a_0 = 2
a
0
=
2
,
a
1
=
5
a_1 = 5
a
1
=
5
, and
a
2
=
8
a_2 = 8
a
2
=
8
, and for
n
>
2
n>2
n
>
2
define
a
n
a_n
a
n
recursively to be the remainder when
4
(
a
n
−
1
+
a
n
−
2
+
a
n
−
3
)
4(a_{n-1} + a_{n-2} + a_{n-3})
4
(
a
n
−
1
+
a
n
−
2
+
a
n
−
3
)
is divided by
11
11
11
. Find
a
2018
⋅
a
2020
⋅
a
2022
a_{2018}\cdot a_{2020}\cdot a_{2022}
a
2018
⋅
a
2020
⋅
a
2022
.
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