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Romanian Masters of Mathematics Collection
2023 Romanian Master of Mathematics Shortlist
A1
A1
Part of
2023 Romanian Master of Mathematics Shortlist
Problems
(1)
Addition respects rationality in polynomials
Source: RMM Shortlist 2023 A1
2/29/2024
Determine all polynomials
P
P
P
with real coefficients satisfying the following condition: whenever
x
x
x
and
y
y
y
are real numbers such that
P
(
x
)
P(x)
P
(
x
)
and
P
(
y
)
P(y)
P
(
y
)
are both rational, so is
P
(
x
+
y
)
P(x + y)
P
(
x
+
y
)
.
Polynomials
algebra
rational number
RMM Shortlist
polynomial