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INMO 2018 -- Problem #4
INMO 2018 -- Problem #4
Source: INMO 2018
January 21, 2018
algebra
Polynomials
Divisibility
Roots of a polynomial
Problem Statement
Find all polynomials with real coefficients
P
(
x
)
P(x)
P
(
x
)
such that
P
(
x
2
+
x
+
1
)
P(x^2+x+1)
P
(
x
2
+
x
+
1
)
divides
P
(
x
3
ā
1
)
P(x^3-1)
P
(
x
3
ā
1
)
.
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