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Contests
National and Regional Contests
Kyrgyzstan Contests
Kyrgyzstan National Olympiad
2010 Kyrgyzstan National Olympiad
5
5
Part of
2010 Kyrgyzstan National Olympiad
Problems
(1)
polynomial equation (KgNM2010)
Source:
4/25/2011
Let
k
k
k
be a constant number larger than
1
1
1
. Find all polynomials
P
(
x
)
P(x)
P
(
x
)
such that
P
(
x
k
)
=
(
P
(
x
)
)
k
P({x^k}) = {\left( {P(x)} \right)^k}
P
(
x
k
)
=
(
P
(
x
)
)
k
for all real
x
x
x
.
algebra
polynomial
function
algebra unsolved