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18
BMT 2022 Guts #18
BMT 2022 Guts #18
Source:
August 31, 2023
number theory
Problem Statement
Nir finds integers
a
0
,
a
1
,
.
.
.
,
a
208
a_0, a_1, ... , a_{208}
a
0
,
a
1
,
...
,
a
208
such that
(
x
+
2
)
208
=
a
0
x
0
+
a
1
x
1
+
a
2
x
2
+
.
.
.
+
a
208
x
208
.
(x + 2)^{208} = a_0x^0 + a_1x^1 + a_2x^2 +... + a_{208}x^{208}.
(
x
+
2
)
208
=
a
0
x
0
+
a
1
x
1
+
a
2
x
2
+
...
+
a
208
x
208
.
Let
S
S
S
be the sum of all an such that
n
−
3
n -3
n
−
3
is divisible by
5
5
5
. Compute the remainder when
S
S
S
is divided by
103
103
103
.
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