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Romanian Masters of Mathematics Collection
2018 Romanian Master of Mathematics
2
Polynomials and powers
Polynomials and powers
Source: RMM 2018 Day 1 Problem 2
February 24, 2018
algebra
polynomial
RMM
RMM 2018
Problem Statement
Determine whether there exist non-constant polynomials
P
(
x
)
P(x)
P
(
x
)
and
Q
(
x
)
Q(x)
Q
(
x
)
with real coefficients satisfying
P
(
x
)
10
+
P
(
x
)
9
=
Q
(
x
)
21
+
Q
(
x
)
20
.
P(x)^{10}+P(x)^9 = Q(x)^{21}+Q(x)^{20}.
P
(
x
)
10
+
P
(
x
)
9
=
Q
(
x
)
21
+
Q
(
x
)
20
.
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