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Romania Team Selection Test
2000 Romania Team Selection Test
2
monic polynomials
monic polynomials
Source: Romanian TST 2000
July 17, 2005
algebra
polynomial
algebra proposed
Problem Statement
Let
P
,
Q
P,Q
P
,
Q
be two monic polynomials with complex coefficients such that
P
(
P
(
x
)
)
=
Q
(
Q
(
x
)
)
P(P(x))=Q(Q(x))
P
(
P
(
x
))
=
Q
(
Q
(
x
))
for all
x
x
x
. Prove that
P
=
Q
P=Q
P
=
Q
.Marius Cavachi
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