MathDB
Problems
Contests
National and Regional Contests
India Contests
India IOQM
2023-24 IOQM India
19
19
Part of
2023-24 IOQM India
Problems
(1)
IOQM 2023-24 P-19
Source:
9/3/2023
For
n
∈
N
n \in \mathbb{N}
n
∈
N
, let
P
(
n
)
P(n)
P
(
n
)
denote the product of the digits in
n
n
n
and
S
(
n
)
S(n)
S
(
n
)
denote the sum of the digits in
n
n
n
. Consider the set
A
=
{
n
∈
N
:
P
(
n
)
A=\{n \in \mathbb{N}: P(n)
A
=
{
n
∈
N
:
P
(
n
)
is non-zero, square free and
S
(
n
)
S(n)
S
(
n
)
is a proper divisor of
P
(
n
)
}
P(n)\}
P
(
n
)}
. Find the maximum possible number of digits of the numbers in
A
A
A
.