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2015 Belarus Team Selection Test
4
p(x^2)=p(x)q(1-x)+p(1-x)q(x)
p(x^2)=p(x)q(1-x)+p(1-x)q(x)
Source: 2015 Belarus TST 2.4
November 5, 2020
polynomial
algebra
Problem Statement
Find all pairs of polynomials
p
(
x
)
,
q
(
x
)
∈
R
[
x
]
p(x),q(x)\in R[x]
p
(
x
)
,
q
(
x
)
∈
R
[
x
]
satisfying the equality
p
(
x
2
)
=
p
(
x
)
q
(
1
−
x
)
+
p
(
1
−
x
)
q
(
x
)
p(x^2)=p(x)q(1-x)+p(1-x)q(x)
p
(
x
2
)
=
p
(
x
)
q
(
1
−
x
)
+
p
(
1
−
x
)
q
(
x
)
for all real
x
x
x
.I.Voronovich
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