MathDB

For every natural number

x{}

, let

P(x)

be the product of the digits of the number

x{}

. Is there a natural number

n{}

such that the numbers

P(n)

and

P(n^2)

are non-zero squares of natural numbers, where the number of digits of the number

n{}

is equal to (a) 2021 and (b) 2022?

Problem Statement