MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2020 Junior Balkan Team Selection Tests - Moldova
12
12
Part of
2020 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
JBMO TST 2020 - Moldova P12
Source: JBMO TST 2020 Moldova
10/13/2020
Find all numbers
n
∈
N
∗
n \in \mathbb{N}^*
n
∈
N
∗
for which there exists a finite set of natural numbers
A
=
(
a
1
,
a
2
,
.
.
.
a
n
)
A=(a_1, a_2,...a_n)
A
=
(
a
1
,
a
2
,
...
a
n
)
so that for any
k
k
k
(
1
≤
k
≤
n
)
(1\leq k \leq n)
(
1
≤
k
≤
n
)
the number
a
k
a_k
a
k
is the number of all multiples of
k
k
k
in set
A
A
A
.
combinatorics
combinatorics unsolved
unsolved