Question 158
Let's designate through $P(n)$ the product of digits of the integer non-negative number $n$. Prove that sets $A$ and $B$ are unbounded, where:
a. $A = \left\{ \frac{P(n)}{P(n^2)} \right\}$, where $n$ belongs to the set of such whole non-negative numbers that the number $n^2$ does not contain zero in the decimal record;
b. $B = \left\{ \frac{P(n^2)}{P(n)} \right\}$, where $n$ belongs to the set of such whole non-negative numbers that the number $n$ does not contain zero in the decimal record.
a. $A = \left\{ \frac{P(n)}{P(n^2)} \right\}$, where $n$ belongs to the set of such whole non-negative numbers that the number $n^2$ does not contain zero in the decimal record;
b. $B = \left\{ \frac{P(n^2)}{P(n)} \right\}$, where $n$ belongs to the set of such whole non-negative numbers that the number $n$ does not contain zero in the decimal record.