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Undergraduate contests
IMC
2018 IMC
9
9
Part of
2018 IMC
Problems
(1)
IMC 2018 P9
Source: IMC 2018 P9
7/25/2018
Determine all pairs
P
(
x
)
,
Q
(
x
)
P(x),Q(x)
P
(
x
)
,
Q
(
x
)
of complex polynomials with leading coefficient
1
1
1
such that
P
(
x
)
P(x)
P
(
x
)
divides
Q
(
x
)
2
+
1
Q(x)^2+1
Q
(
x
)
2
+
1
and
Q
(
x
)
Q(x)
Q
(
x
)
divides
P
(
x
)
2
+
1
P(x)^2+1
P
(
x
)
2
+
1
.Proposed by Rodrigo Angelo, Princeton University and Matheus Secco, PUC, Rio de Janeiro
college contests
imc2018