MathDB
Problems
Contests
National and Regional Contests
China Contests
ASDAN Math Tournament
2020 ASDAN Math Tournament
10
10
Part of
2020 ASDAN Math Tournament
Problems
(1)
2020 Team #10
Source:
10/24/2023
Let
r
=
1
−
2
5
+
4
5
−
8
5
+
16
5
r = 1-\sqrt[5]{2}+ \sqrt[5]{4}-\sqrt[5]{8}+ \sqrt[5]{16}
r
=
1
−
5
2
+
5
4
−
5
8
+
5
16
. There exists a unique fifth-degree polynomial
P
P
P
such that its leading coefficient is positive, all of its coefficients are integers whose greatest common factor (among all of them) is
1
1
1
, and
P
(
r
)
=
0
P(r) = 0
P
(
r
)
=
0
. Evaluate
P
(
10
)
P(10)
P
(
10
)
.
team test