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Middle European Mathematical Olympiad
2017 Middle European Mathematical Olympiad
1
Polynomial FE
Polynomial FE
Source: MEMO 2017 T1
August 25, 2017
algebra
polynomial
Problem Statement
Determine all pairs of polynomials
(
P
,
Q
)
(P, Q)
(
P
,
Q
)
with real coefficients satisfying
P
(
x
+
Q
(
y
)
)
=
Q
(
x
+
P
(
y
)
)
P(x + Q(y)) = Q(x + P(y))
P
(
x
+
Q
(
y
))
=
Q
(
x
+
P
(
y
))
for all real numbers
x
x
x
and
y
y
y
.
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