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National and Regional Contests
Azerbaijan Contests
Azerbaijan Senior National Olympiad
2023 Azerbaijan Senior NMO
3
3
Part of
2023 Azerbaijan Senior NMO
Problems
(1)
all polynomials depending on m
Source: Azerbaijan NMO 2023. Senior P3
8/24/2023
Let
m
m
m
be a positive integer. Find polynomials
P
(
x
)
P(x)
P
(
x
)
with real coefficients such that
(
x
ā
m
)
P
(
x
+
2023
)
=
x
P
(
x
)
(x-m)P(x+2023) = xP(x)
(
x
ā
m
)
P
(
x
+
2023
)
=
x
P
(
x
)
is satisfied for all real numbers
x
.
x.
x
.
algebra
AZE SENIOR NATIONAL MO
polynomial