Question 30
Let $x$, $y$ be two unknown natural numbers less than $100!$. Prove that there are natural numbers $m$ and $n$ such that knowing the value of $\varphi(d(my)) + d(\varphi(nx))$ would lead to the unique determination of the values $x$ and $y$.
(Note. $\varphi(n)$ is the number of positive integers that are less than and co-prime to $n$, and $d(n)$ is the number of positive divisors of $n$.)
(Note. $\varphi(n)$ is the number of positive integers that are less than and co-prime to $n$, and $d(n)$ is the number of positive divisors of $n$.)