MathDB
Problems
Contests
Undergraduate contests
Putnam
2021 Putnam
A5
A5
Part of
2021 Putnam
Problems
(1)
Putnam 2021 A5
Source:
12/5/2021
Let
A
A
A
be the set of all integers
n
n
n
such that
1
≤
n
≤
2021
1 \le n \le 2021
1
≤
n
≤
2021
and
gcd
(
n
,
2021
)
=
1
\text{gcd}(n,2021)=1
gcd
(
n
,
2021
)
=
1
. For every nonnegative integer
j
j
j
, let
S
(
j
)
=
∑
n
∈
A
n
j
.
S(j)=\sum_{n \in A}n^j.
S
(
j
)
=
n
∈
A
∑
n
j
.
Determine all values of
j
j
j
such that
S
(
j
)
S(j)
S
(
j
)
is a multiple of
2021
2021
2021
.
Putnam
Putnam 2021