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Serbia National Math Olympiad
2024 Serbia National Math Olympiad
6
6
Part of
2024 Serbia National Math Olympiad
Problems
(1)
NT with iteration of polynomial and perfect squares
Source: Serbia 2024 MO Problem 6
4/4/2024
Find all non-constant polynomials
P
(
x
)
P(x)
P
(
x
)
with integer coefficients and positive leading coefficient, such that
P
2
m
n
(
m
2
)
+
n
2
P^{2mn}(m^2)+n^2
P
2
mn
(
m
2
)
+
n
2
is a perfect square for all positive integers
m
,
n
m, n
m
,
n
.
number theory