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2023 MOAA
23
23
Part of
2023 MOAA
Problems
(1)
2023 MOAA Gunga P23
Source:
10/15/2023
For every positive integer
n
n
n
let
f
(
n
)
=
n
4
+
n
3
+
n
2
−
n
+
1
n
6
−
1
f(n) = \frac{n^4+n^3+n^2-n+1}{n^6-1}
f
(
n
)
=
n
6
−
1
n
4
+
n
3
+
n
2
−
n
+
1
Given
∑
n
=
2
20
f
(
n
)
=
a
b
\sum_{n = 2}^{20} f(n) = \frac{a}{b}
n
=
2
∑
20
f
(
n
)
=
b
a
for relatively prime positive integers
a
a
a
and
b
b
b
, find the sum of the prime factors of
b
b
b
.Proposed by Harry Kim
MOAA 2023