MathDB

A positive integer

m

is said to be \emph{zero taker} if there exists a positive integer

k

such that:

k

is a perfect square;

m

divides

k

; the decimal expression of

k

contains at least

2021

'0' digits, but the last digit of

k

is not equal to

0

.
Find all positive integers that are zero takers.

1