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Problems
Contests
National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
2021 Ukraine National Mathematical Olympiad
11.1
11.1
Part of
2021 Ukraine National Mathematical Olympiad
Problems
(1)
a_{2021}n^{2021}+a_{2020}n^{2020}+...+a_1n+a_0 divisible by 2021
Source: 2021 Ukraine NMO 11.1
4/2/2021
It is known that for some integers
a
2021
,
a
2020
,
.
.
.
,
a
1
,
a
0
a_{2021},a_{2020},...,a_1,a_0
a
2021
,
a
2020
,
...
,
a
1
,
a
0
the expression
a
2021
n
2021
+
a
2020
n
2020
+
.
.
.
+
a
1
n
+
a
0
a_{2021}n^{2021}+a_{2020}n^{2020}+...+a_1n+a_0
a
2021
n
2021
+
a
2020
n
2020
+
...
+
a
1
n
+
a
0
is divisible by
2021
2021
2021
for any arbitrary integer
n
n
n
. Is it required that each of the numbers
a
2021
,
a
2020
,
.
.
.
,
a
1
,
a
0
a_{2021},a_{2020},...,a_1,a_0
a
2021
,
a
2020
,
...
,
a
1
,
a
0
also divisible by
2021
2021
2021
?
number theory