Question 104
Call a positive integer in base $10$ $k$-good if we can split it into two integers $y$ and $z$, such that $y$ is all digits on the left and $z$ is all digits on the right, and such that $y = k \cdot z$. For example, $2010$ is $2$-good because we can split it into $20$ and $10$ and $20 = 2 \cdot 10$. $20010$ is also $2$-good, because we can split it into $20$ and $010$. In addition, it is $20$-good, because we can split it into $200$ and $10$.
Show that there exists a $48$-good perfect square.
Show that there exists a $48$-good perfect square.