MathDB

Call a super-integer an infinite sequence of decimal digits:

\ldots d_n \ldots d_2d_1

.
(Formally speaking, it is the sequence

(d_1,d_2d_1,d_3d_2d_1,\ldots)

)
Given two such super-integers

\ldots c_n \ldots c_2c_1

and

\ldots d_n \ldots d_2d_1

, their product

\ldots p_n \ldots p_2p_1

is formed by taking

p_n \ldots p_2p_1

to be the last n digits of the product

c_n \ldots c_2c_1

and

d_n \ldots d_2d_1

. Can we find two non-zero super-integers with zero product? (a zero super-integer has all its digits zero)

Problem Statement