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Grosman Mathematical Olympiad
2023 Grosman Mathematical Olympiad
3
Product of polynomials equals composition
Product of polynomials equals composition
Source: 2023 Grosman MO, P3
September 8, 2023
algebra
polynomial
composition
Problem Statement
Find all pairs of polynomials
p
p
p
,
q
q
q
with complex coefficients so that
p
(
x
)
ā
q
(
x
)
=
p
(
q
(
x
)
)
.
p(x)\cdot q(x)=p(q(x)).
p
(
x
)
ā
q
(
x
)
=
p
(
q
(
x
))
.
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