MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CHMMC problems
2021 CHMMC Winter (2021-22)
6
2021-22 Winter Team #6
2021-22 Winter Team #6
Source:
April 17, 2022
number theory
algebra
Problem Statement
There is a unique degree-
10
10
10
monic polynomial with integer coefficients
f
(
x
)
f(x)
f
(
x
)
such that
f
(
∑
j
=
0
9
202
1
j
10
)
=
0.
f \left( \sum^9_{j=0}\sqrt[10]{2021^j}\right)= 0.
f
(
j
=
0
∑
9
10
202
1
j
)
=
0.
Find the remainder when
f
(
1
)
f(1)
f
(
1
)
is divided by
1000
1000
1000
.
Back to Problems
View on AoPS