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Poland - Second Round
1970 Poland - Second Round
5
Q(x) = P(x) P(x^3) P(x^9) P(x^{27}) P(x^{81})
Q(x) = P(x) P(x^3) P(x^9) P(x^{27}) P(x^{81})
Source: Polish MO second round 1970 p5
August 28, 2024
algebra
polynomial
Problem Statement
Given the polynomial
P
(
x
)
=
1
2
−
1
3
x
+
1
6
x
2
P(x) = \frac{1}{2} - \frac{1}{3}x + \frac{1}{6}x^2
P
(
x
)
=
2
1
−
3
1
x
+
6
1
x
2
. Let
Q
(
x
)
=
∑
k
=
0
m
b
k
x
k
Q(x) = \sum_{k=0}^{m} b_k x^k
Q
(
x
)
=
∑
k
=
0
m
b
k
x
k
be a polynomial given by
Q
(
x
)
=
P
(
x
)
⋅
P
(
x
3
)
⋅
P
(
x
9
)
⋅
P
(
x
27
)
⋅
P
(
x
81
)
.
Q(x) = P(x) \cdot P(x^3) \cdot P(x^9) \cdot P(x^{27}) \cdot P(x^{81}).
Q
(
x
)
=
P
(
x
)
⋅
P
(
x
3
)
⋅
P
(
x
9
)
⋅
P
(
x
27
)
⋅
P
(
x
81
)
.
Calculate
∑
k
=
0
m
∣
b
k
∣
\sum_{k=0}^m |b_k|
∑
k
=
0
m
∣
b
k
∣
.
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