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3
2022 PUMaC Team #3
2022 PUMaC Team #3
Source:
September 9, 2023
algebra
Problem Statement
Provided that
{
a
i
}
i
=
1
28
\{a_i\}^{28}_{i=1}
{
a
i
}
i
=
1
28
are the
28
28
28
distinct roots of
29
x
28
+
28
x
27
+
.
.
.
+
2
x
+
1
=
0
29x^{28} + 28x^{27} + ... + 2x + 1 = 0
29
x
28
+
28
x
27
+
...
+
2
x
+
1
=
0
, then the absolute value of
∑
i
=
1
28
1
(
1
−
a
i
)
2
\sum^{28}_{i=1}\frac{1}{(1-a_i)^2}
∑
i
=
1
28
(
1
−
a
i
)
2
1
can be written as
p
q
\frac{p}{q}
q
p
for relatively prime positive integers
p
,
q
p, q
p
,
q
. Find
p
+
q
p + q
p
+
q
.
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