Question 7
Call a super-integer an infinite sequence of decimal digits: $\ldots d_n \ldots d_3 d_2 d_1$. Given two super-integers $\ldots c_n \ldots c_3 c_2 c_1$ and $\ldots d_n \ldots d_3 d_2 d_1$, their product $\ldots p_n \ldots p_3 p_2 p_1$ is formed by taking $p_n \ldots p_3 p_2 p_1$ to be the last $n$ digits of the product $c_n \ldots c_3 c_2 c_1$ and $d_n \ldots d_3 d_2 d_1$. Can we find two non-zero super-integers with zero product? A zero super-integer has all its digits zero.