MathDB
Problems
Contests
Undergraduate contests
IMC
2000 IMC
2
find all pairs
find all pairs
Source: IMC 2000 day 1 problem 2
October 29, 2005
complex analysis
complex analysis unsolved
Problem Statement
Let
p
(
x
)
=
x
5
+
x
p(x)=x^5+x
p
(
x
)
=
x
5
+
x
and
q
(
x
)
=
x
5
+
x
2
q(x)=x^5+x^2
q
(
x
)
=
x
5
+
x
2
, Find al pairs
(
w
,
z
)
∈
C
×
C
(w,z)\in \mathbb{C}\times\mathbb{C}
(
w
,
z
)
∈
C
×
C
,
w
≠
z
w\not=z
w
=
z
for which
p
(
w
)
=
p
(
z
)
,
q
(
w
)
=
q
(
z
)
p(w)=p(z),q(w)=q(z)
p
(
w
)
=
p
(
z
)
,
q
(
w
)
=
q
(
z
)
.
Back to Problems
View on AoPS