MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2018 India National Olympiad
4
4
Part of
2018 India National Olympiad
Problems
(1)
INMO 2018 -- Problem #4
Source: INMO 2018
1/21/2018
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
)
.
algebra
Polynomials
Divisibility
Roots of a polynomial